What is the source of this famous verse?

Question

आकाशात् पतितं तोयं यथा गच्छति सागरम् ।
सर्वदेवनमस्कारं केशवं प्रतिगच्छति ॥

ākāśāt patitaṃ toyaṃ yathā gacchati sāgaram ।
sarvadevanamaskāraṃ keśavaṃ pratigacchati ॥

Meaning:

As the water that falls down in rain from anywhere in the sky finally reaches the Ocean, the worship of any divine aspect ultimately reaches the Supreme Being.

The above verse is quite famous. This shloka is used by many to prove the oneness of the God.

• From which scripture is the above verse taken?
  
• If the verse is not one from any veda or upanishad, then who is the author of it?

^{Translation from this blog}

Answer 1

The śloka appears to be from the end of Viṣṇusahasranāma belonging to a recension of the Mahābhārata that did not make it to the BORI critical edition:

13,135.142d*0637_06   rudra uvāca

13,135.142d*0637_07   rāma rāmeti rāmeti rame rāme manorame
13,135.142d*0637_08   śrīsahasranāmatattulyaṃ rāmanāma varānane

13,135.142d*0638_01   iti stutvā hṛṣīkeśaṃ pārthas tūṣṇīṃ sthitas tataḥ
13,135.142d*0639_01   namo brahmaṇyadevāya gobrāhmaṇahitāya ca
13,135.142d*0639_02   jagaddhitāya kṛṣṇāya govindāya namo namaḥ

13,135.142d*0639_03   ākāśāt patitaṃ toyaṃ yathā gacchati sāgaram
13,135.142d*0639_04   sarvadevanamaskāraḥ keśavaṃ prati gacchati

13,135.142d*0639_05   sarvavedeṣu yat puṇyaṃ sarvavedeṣu yat phalam
13,135.142d*0639_06   tat phalaṃ puruṣa āpnoti stutvā devaṃ janārdanam

13,135.142d*0640_01   jitaṃ te puṇḍarīkākṣa namas te viśvabhāvana
13,135.142d*0640_02   namas te 'stu hṛṣīkeśa mahāpuruṣapūrvaja

This question states that a slightly different version of Viṣṇusahasranāma is also part of Padma and Skanda Purāṇas but I didn't find the śloka in those.

Answer 2

The verse appears to be present in a certain smriti text by the name of Laugakshi Smriti.

Answer 3

Deeply analysing;

जगतः कस्मिन् अपि कोणे आकाशात् पतति प्रत्येकं जलबिन्दुः अन्ते समुद्रेण सह सम्मिलितः भवति, तथैव जगतः कस्मिन् अपि कोणे केनचित् रूपेण केनचित् नाम्ना कस्यापि देवस्य पूजिताः प्रार्थनाः अन्ते परमेश्वरं विष्णुं प्राप्नुवन्ति

Just as every drop of water falling from the sky in any corner of the world eventually reaches the ocean, similarly, the prayers offered to any god in any name, or form, in any corner of the world ultimately reach the Supreme Lord Vishnu.