India are 1-0 ahead in the five-match series.
West Indies batsman S Hope scored 123 not out and S Hetmyer (94) fell short of scoring a century.
While he acknowledged the fans' applause by raising his bat after reaching the 10k landmark, the crowd was on its feet again when Kohli creamed Marlon Samuels to the cover boundary to bring up his century, his 37th in this format.
"It's just one game (the first ODI in Guwahati), I think they bowled really well and it's just that Virat and Rohit batted brilliantly".
"I never thought of achieving this feat, or get to this stage, I always thought I want to play for India".
Kohli also took over Tendulkar's aggregate of 1,573 to become India's highest run-getter in ODIs against the Windies.
The 29-year-old passed the mark in his 205th innings - smashing the previous best of 259 set by Tendulkar against Australia in Indore in 2001 - en route to an unbeaten 157 from 129 deliveries as India posted 321-6, Aambati Rayudu contributing 73.
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One photo showed the son, Salah, looking ashen-faced and shaking hands with Mohammed as a video cameraman stood in the background. He added: "I will not allow a wedge to form between Saudi Arabia and Turkey".
Left-arm wrist spinner Kuldeep Yadav claimed three wickets in what turned out to be the second tied game between the two sides.
And with reaching 10,000 runs, Kohli will join the elite club that till today has only four Indian, and overall 12 batsmen from around the world.
"However, I must accept that for me to preserve my longevity as a professional cricketer, I must do as others before have done, leave the global arena for the next generation of players".
With just 17 One-day Internationals (ODI) to be played till the 2019 ICC World Cup in England and Wales, newly anointed India's No.4 Ambati Rayudu on Tuesday said the responsibility of batting in the middle order isn't something "new" for him and that he is not looking too far ahead.
"Shai Hope is a young talent and he played a magnificent knock..."
West Indies skipper Jason Holder said his runout and the fall of Shimron Hetmyer were the turning points of the match. Nurse was the pick of the West Indies bowlers with his figures of 2-46.