The two marauding batsmen started to toy with the opposition bowlers before Devendra Bishoo got Kohli stumped against the run of play.
Windies batsman Shimron Hetmyer's 74-ball ton had set the hosts a seemingly challenging chase in the first game of the five-match series, only for Kohli (140 off 107 balls) and Rohit (152no off 117) to break the back of India's reply after Shikhar Dhawan (4) fell in the second over to debutant Oshane Thomas.
Kohli pounded the Caribbean bowlers with 21 fours and two sixes to raise his 36th ODI century and now needs just 81 runs to join the elite club of cricketers who have amassed 10,000 runs in the One-day format.
Rohit, who boasts three double hundreds in ODIs, grew in confidence as he spent time at the crease and cleared the boundary rope easily when he looked to attack, hitting 15 boundaries and eight sixes, the last of which brought up India's victory.
"But we knew it's all about one partnership".
"Among the top three, I mostly take the anchor role because both Rohit and Shikhar (Dhawan) are good stroke-makers", he said.
"When (Ambati) Rayudu came he took that role and Rohit took over from me".
"It's our 5th or 6th double-century partnership, it's a pleasure to bat with him (Rohit)".
This partnership is also India's highest while chasing as they went past Gautam Gambhir and Virat Kohli who posted 224 runs against Sri Lanka in Kolkata in 2009.
"I have few years left in my career to enjoy this sport". That's my basic thinking, because you are playing for India and not everyone gets to do that. It's hard to contain when a side like West Indies bats like that.
Jadeja and Yuzvendra Chahal (3-41) stemmed the run rate with the latter accounting for Holder and Ashley Nurse (2), only for Bishoo and Roach to frustrate India, who beat Windies 2-0 in the preceding Test series following thumping wins in Rajkot and Hyderabad.