Since the question has the tag Adi-Shankaracharya, I am quoting some of the Bhashyas (commentaries) of Adi Shankara, that are widely accepted as authentic. However, I have intentionally refrained from quoting Shankara's Bhagavad Gita bhashya, even though it is also widely regarded as authentic. The below quotes focus on Vishnu alone, and I am not suggesting any implication from these quotes for either Brahma or Shiva or any other God/Goddess. So please dont read sectarianism into my answer.
Brahmasutra Bhashya (BSB) 2.1.1 and translation by George Thibaut
अतश्च संक्षेपमिमं शृणुध्वं नारायणः सर्वमिदं पुराणः । स सर्गकाले च करोति सर्वं संहारकाले च तदत्ति भूयः’ इति पुराणे
Thus we read also in the Purâna, 'Hear thence this short statement: The ancient Nârâyana is all this; he produces the creation at the due time, and at the time of reabsorption he consumes it again
तत्र यत्तावदुच्यते — योऽसौ नारायणः परोऽव्यक्तात्प्रसिद्धः परमात्मा सर्वात्मा, स आत्मनात्मानमनेकधा व्यूह्यावस्थित इति — तन्न निराक्रियते, ‘ स एकधा भवति त्रिधा भवति’ (छा. उ. ७ । २६ । २) इत्यादिश्रुतिभ्यः परमात्मनोऽनेकधाभावस्याधिगतत्वात् ;
यदपि तस्य भगवतोऽभिगमनादिलक्षणमाराधनमजस्रमनन्यचित्ततयाभिप्रेयते, तदपि न प्रतिषिध्यते, श्रुतिस्मृत्योरीश्वरप्रणिधानस्य प्रसिद्धत्वात्
Concerning this system we remark that we do not intend to controvert the doctrine that Nârâyana, who is higher than the Undeveloped, who is the highest Self, and the Self of all, reveals himself by dividing himself in multiple ways; for various scriptural passages, such as 'He is onefold, he is threefold' (Kh. Up. VII, 26, 2)', teach us that the highest Self appears in manifold forms. Nor do we mean to object to the inculcation of unceasing concentration of mind on the highest Being which appears in the Bhâgavata doctrine under the forms of reverential approach,for that we are to meditate on the Lord we know full well from Smriti and Scripture.
कार्यब्रह्मलोकप्रलयप्रत्युपस्थाने सति तत्रैव उत्पन्नसम्यग्दर्शनाः सन्तः, तदध्यक्षेण हिरण्यगर्भेण सह अतः परं परिशुद्धं विष्णोः परमं पदं प्रतिपद्यन्ते
When the reabsorption of the effected Brahman world draws near, the souls in which meanwhile perfect knowledge has sprung up proceed, together with Hiranyagarbha the ruler of that world, to 'what is higher than that i.e. to the pure highest place of Vishnu.
Brihadaranyana upanishad Bhashya 3.7.3 and translation by Swami Madhavananda
य ईदृगीश्वरो नारायणाख्यः, पृथिवीं पृथिवीदेवताम् , यमयति नियमयति स्वव्यापारे, अन्तरः अभ्यन्तरस्तिष्ठन् , एष त आत्मा, ते तव, मम च सर्वभूतानां च इत्युपलक्षणार्थमेतत् , अन्तर्यामी यस्त्वया पृष्टः, अमृतः सर्वसंसारधर्मवर्जित इत्येतत्
Such an īśvara, called Nāràyana, who controls the deity of the earth, i.e. directs her to her particular work, from within, is the Internal Ruler about whom you have asked, your own immortal self, as also mine and that of all beings. ‘Your’ implies ‘others’ as well. ‘Immortal,’ that is to say, devoid of all relative attributes.
Mandukya upanishad and Gaudapada Karika bhashya (4.1, Gaudapada Karika), translated by Swami Nikhilananda
ज्ञेयैर्धर्मैरात्मभिरभिन्नम् अग्न्युष्णवत् सवितृप्रकाशवच्च यत् ज्ञानम् , तेन ज्ञेयाभिन्नेन ज्ञानेन आकाशकल्पेन ज्ञेयात्मस्वरूपाव्यतिरिक्तेन, गगनोपमान्धर्मान्यः सम्बुद्धः सम्बुद्धवान्नित्यमेव ईश्वरो यो नारायणाख्यः, तं वन्दे अभिवादये । द्विपदां वरं द्विपदोपलक्षितानां पुरुषाणां वरं प्रधानम् , पुरुषोत्तममित्यभिप्रायः ।
I bow to the God, known as Nārāyaṇa, who by knowledge, non-different from the nature of Ātman (the object of knowledge) and which resembles Ākāśa, knew the Dharmas which, again, may be compared to Ākāśa. The import of the words “Dvipadām Varam” (Supreme among the bipeds), is that Nārāyaṇa is the greatest of all men, characterised by two legs, that, is to say, He is the “Puruṣottama”, the best of all men.
Mundaka upanishad bhashya (2.1.4) translated by Swami Gambhirananda
यस्य च पद्भ्यां जाता पृथिवी, एष देवो विष्णुरनन्तः प्रथमशरीरी त्रैलोक्यदेहोपाधिः सर्वेषां भूतानामन्तरात्मा । स हि सर्वभूतेषु द्रष्टा श्रोता मन्ता विज्ञाता सर्वकरणात्मा ॥
And from whose two feet, the earth is born. This one - the deity who is Vishnu (the all-pervading), or Ananta (the infinite), the first embodied Being who has the three worlds as his physical limiting adjunct - is the indwelling Self of all.
From the above quotes it is clear that Shankara considered Vishnu/Narayana as brahman. The implication is that Vishnu cannot be subjected to karma, as per Shankara.
Addition to the answer - Part 2
Ok, so if Vishnu is supreme, why does the Devi Bhagavatam say that Vishnu is subject to karma. The answer for these kind of questions is nahi ninda nyAya as explained by Kanchi paramAchArya -
Each Purana is in the main devoted to a particular devata. In the Siva Purana it is stated: "Siva is the Supreme Being. He is the highest authority for creation, sustenance and dissolution. It is at his behest, and under him, that Visnu funtions as protector. Visnu is a mere bhogin, trapped in Maya. Siva is a yogin and jnana incarnate. Visnu is subject to Siva and worships him. Once when he opposed Siva he suffered humiliation at his hands". Stories are told to illustrate such assertions.
In the Vaisnava Puranas you see the reverse. They contain stories to support the view that Visnu is superior to Siva. "Is Siva a god, he who dwells in the burning grounds with spirits and goblins for company? " these Puranas ask.
In each Purana thus a particular deity is exalted over others. It may be Subrahmanya, Ganapati or Surya. Each such deity is declared to be the Supreme God and all others are said to worship him. When, out of pride, they refuse to worship him they are humbled.
Doubts arise in our minds about such contradictory accounts. "Which of these stories is true? " we are inclined to ask. "And which is false? They cannot all of them be true. If Siva worships Visnu, how does it stand to reason that Visnu should adore Siva? If Amba is superior to the Trimurti (Brahma, Visnu and Mahesvara), how is it right to say that she remains submissive to Parameswara as his devoted consort? The Puranas cannot all of them be true. Or are they all lies? "
Logical thinking seems to point to the conclusion that all Puranic stories cannot be true. But, as a matter of fact, they are. A deity that suffers defeat at one time at the hands of another emerges triumphant on another occasion. And a god who worships another deity is himself the object of worship at other times. How is this so and why?
The Paramatman is one and only one. He it is that creates, sustains and destroys. And it is he who exfoliates as the the many different deities. Why does he do so? He has not cast people in the same mould. He has created them all differently, with different attitudes, the purpose being to make the affairs of the world interesting by imparting variety to them. The Paramatman himself assumes different forms to suit the temperament of different people so that each worship him in the form he likes and obtain happiness. This is the reason why the one and only Paramatman manifests himself as so many different deities.
Everybody must have firm faith in, and devotion for, his chosen deity. He must learn to believe that this deity of his is the Paramatman, that there is no power higher. That is the reason why each manifestation or form of the Supreme Godhead reveals itself to be higher than other forms or manifestations. It is thus that these other forms are shown to have worshipped it or suffered defeat at its hands. Altogether it means that each deity worships other deities and is in turn worshipped by others. Also each god suffers defeat at the hands of other gods and, at the same time, inflicts defeat on them.
In the Saiva Puranas all those aspects that proclaim the glory of Siva are brought together. Similarly, in the case of the Vaisnava Puranas that deal with Visnu. Amba, Subrahmanya and other deities are each of them dealt with in such a way as to show him or her to be the highest among the devatas.
The purpose of exalting a particular deity over the another is not to depreciate the latter. The underlying idea is that a person who worships his chosen god has unflinching faith in him and becomes totally devoted to him. Such exclusive devotion is called "ananyabhakti". The idea here, however, is not to regard other devatas as inferior to one's own chosen deity- an example of "nahi ninda nyaya".
Those who are capable of looking upon all deities as the manifestations of the one and only Paramatman have no cause for exclusive devotion to any one of them. It is only when we think that one deity is separate from- or alien to- another that the question arises of giving up one for another. If we realise that all are the different disguises of the One Reality, the various gods and goddesses potrayed in the Puranas, with all the differences among them, will be understood to be nothing but the lila or sport of Supreme Being. It is the One alone that seems divided into manifold entities. This is to help men of various attitudes and temperaments. If this truth is recognised we shall be able to see the stories in the Puranas- stories that seem contradictory- in the true light.
In the story of Banasura we see that Siva is vanquished by Krsna. But in the story of Tiruvannamalai, Visnu meets with failure in finding the feet of Siva. Both stories must be treated as truthful. The first is to make devotees of Krsna worship him as the Paramatman and the second to make devotees of Siva adore him similarly. Although we think that one is winner and the other the loser or that the one is superior to the other or inferior to him, the two know themselves to be one. Does one triumph over oneself- or does one inflict defeat upon oneself? So all this is play. The Parmatman indulges in sport assuming multifarious forms.
The purpose of the Puranas is to show people the right path. Pativratya is a virtue that is of the utmost importance. Amba herself exemplifies it. The Parasakti, the Supreme Power that she is, remains subject to her husband. Faith and devotion must grow in the world and for it the Lord himself must show the way. This is why in some temples Visnu is represented as a worshipper of Siva and in some other shrines Siva is seen as a devotee of Visnu. The same with other deities. I have spoken more about Siva and Visnu since Saivism and Vaisnavism are the two major divisions.
To sum up, if a deity is glorified in the Puranas, and stories told in support of it, it is to create exclusive devotion to him as the Paramatman. And, if any god is potrayed as inferior to another, the true purpose of it is not to denigrate him but to develop unflinching faith in the latter.
Looked at from the above angle, the Devi Bhagavatam is saying Brahma, Vishnu, Shiva and others as subject to karma, not with the intention of denigrating them, but with the intention of extolling Devi as the supreme brahman (and as the one who controls even the trimurtis by subjecting them to karma) and helping the devotee of Devi to develop devotion for her. The truth is that none of the trimurtis are subjected to karma and none of them are sinners. This is an example of nahi ninda nyAya. These statements of Devi bhAgavatam must be seen in this light, as per the explanation of Kanchi paramAchArya.