The Supreme Personality of Godhead (Lord Nārāyaṇa) said to the brāhmaṇa (Durvāsā Muni): I am completely under the control of My devotees. Indeed, I am not at all independent. Because My devotees are completely devoid of material desires, I sit only within the cores of their hearts. What to speak of My devotee, even those who are devotees of My devotee are very dear to Me.
As chaste women bring their gentle husbands under control by service, the pure devotees, who are equal to everyone and completely attached to Me in the core of the heart, bring Me under their full control.
To understand such shlokas in more details, you can read commentaries on them. When you open these shloka link from here, commentaries can be found or you can read commentaries from some other sources.
As given in other answers, devotees can control Lord Krishna. A very similar verse which user YDS quoted in answer is also mentioned in Vasudeva Mahatmyam, chapter - 18: The narration of the incarnations of Sri Vasudeva. Vasudeva Mahatmyam is a part of Skanda purana (volume 6).
In this, Lord Krishna tells sage Narada,
You are my intimate devotee with a sincere inner self. Hence, I feel that you are greater than your father Brahma. (60)
Oh, Sage! In whatever form I may be, My supremacy is always known to my intimate devotees. (61)
Good people think of me from within their hearts and, I too think of them, My devotees. They like nothing else other than Me. I have no liking for anything except them. Just as chaste women control their husbands by means of their qualities, so also My devotees control Me by their qualities. (62-63)
In his Stotra-ratna (15), Yāmunācārya praises the Lord as follows:
vasi vadanyo gunavan njuh sucir
mridur dayalur madhurah sthirah samah
kriti kritajnas tvam asi sva-bhavatah
You are naturally controlled by the love of Your devotees, generous, virtuous, straightforward, honest, pure, gentle, merciful, charming, steadfast, equal to all, blissful, wise, and saintly. You are a nectar ocean of all auspicious transcendental qualities.
As this holds true for a devotee in general, it must also hold true for Radha, as She is the topmost devotee of Krishna
This is a recurring theme throughout the scriptures. Krishna says in the Uddhava Gita, Chapter 9 (Uddhava Gita is in the 11th book of the Bhagavata), Swami Madhavananda translator:
Neither Brahma, nor Shiva, nor Balarama, nor Lakshmi, nor My own form is so dear to Me as you. [addressing Uddhava, who Krishna says is the supreme devotee of the Lord]
With a view to purifying Myself by the dust of his feet, I always follow the sage who cares for nothing, is calm, bears enmity to none, and is even-minded.
O Uddhava, neither Yoga, nor knowledge, nor piety, nor study, nor austerity, nor renunciation captivates Me so much as a heightened devotion to Me.
And in the Gita (Swami Nikhilananda translator):
VI. 30. He who sees Me everywhere and sees everything in Me, to him I am never lost, nor is he ever lost to Me.
VI. 31. He who having been established in oneness, worships Me dwelling in all beings--that yogi, in whatever way he leads his life, lives in Me.
VII. 17. ...For supremely dear am I to the man of wisdom, and he is dear to Me.
IX. 29. I am the same to all beings; to Me there is none hateful or dear. But those who worship Me with devotion--they are in Me, and I too am in them.
The Lord cannot resist true Bhakti, true love which asks for nothing in return. He is drawn to true love as iron is drawn to a magnet. Thus, as it says in the Uddhava Gita, he follows a true sage in order to get the dust of his feet.
Yes, Bhakti can control Krishna and bhakti alone can control Krishna.
SB 11.14.20: My dear Uddhava, the unalloyed devotional service
rendered to Me by My devotees brings Me under their control. I cannot
be thus controlled by those engaged in mystic yoga, Sāṅkhya
philosophy, pious work, Vedic study, austerity or renunciation.
SB 9.4.63: The Supreme Personality of Godhead said to the brāhmaṇa: I
am completely under the control of My devotees. Indeed, I am not at
all independent. Because My devotees are completely devoid of material
desires, I sit only within the cores of their hearts. What to speak of
My devotee, even those who are devotees of My devotee are very dear to
We don't get explicit mention of Radha, but we can see how Krishna is controlled by devotees of Vrindavan:
SB 10.11.7:(The gopīs would say, “If You dance, my dear Kṛṣṇa, then I
shall give You half a sweetmeat.” By saying these words or by clapping
their hands)all the gopīs encouraged Kṛṣṇa in different ways. At such
times, although He was the supremely powerful Personality of Godhead,
He would smile and dance according to their desire, as if He were a
wooden doll in their hands. Sometimes He would sing very loudly, at
their bidding. In this way, Kṛṣṇa came completely under the control of
SB 10.11.9: To pure devotees throughout the world who could understand
His activities, the Supreme Personality of Godhead, Kṛṣṇa, exhibited
how much He can be subdued by His devotees, His servants. In this way
He increased the pleasure of the Vrajavāsīs by His childhood
SB 10/9/19: O Mahārāja Parīkṣit, this entire universe, with its great,
exalted demigods like Lord Śiva, Lord Brahmā and Lord Indra, is under
the control of the Supreme Personality of Godhead. Yet the Supreme
Lord has one transcendental attribute: He comes under the control of
His devotees. This was now exhibited by Kṛṣṇa in this pastime.
As mentioned in the Brahmasamhita, "Ananda chinmaya rasa pratibhavitabhih, tabhirya eva nij-roop taya kalabhi", (B.S.5.37), SriRadha is a personal (transcendental potency) form of Krishna Himself who has sixtyfour qualities of Krishna's infinite eternal qualities. Krishna is also known for His, "kartum, akartum, anyathakartum saamarthaya". He can do whatever He wants to do, He can do other ways, He can do what no one has done before. Radha is the transcendental personification of His personal potency which He manifests to do something out of the way.
So, this way if She controls Him means Krishna can only be controlled by Himself, as SriRadha.
Nevertheless, in the Bhagvatam ninth canto (skand) in chapter four (durvasa-muni and king-amberish episode) He has also conclusively mentioned , "aham bhakt paradhino". He is never controlled, however, His innocent and pure devotee unknowingly controls Him in the eternal love.
śrī-bhagavān uvāca — Sri Bhagvan said; aham — I; bhakta-parādhīnaḥ — am dependent on the will of My devotees; hi — indeed; asvatantraḥ — am not independent; iva — exactly like that; dvija — O brāhmaṇa; sādhubhiḥ — by pure devotees, completely free from all material desires; grasta-hṛdayaḥ — My heart is controlled; bhaktaiḥ — because they are devotees; bhakta-jana-priyaḥ — I am dependent not only on My devotee but also on My devotee’s devotee (the devotee’s devotee is extremely dear to Me).
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