Sammy clobbered 41 off 17 balls and Russell smashed 40 off 18, together scoring 79 from just 34 balls in the final overs.[break]
India, which is looking to take a winning 3-0 lead in the five-game series after winning the opening two games, failed to stop the pair after seemingly taking control of the West Indies innings.
Sammy and Russell were helped by some wayward bowling as Abhimanyu Mithun went for 23 runs in the 49th over and Umesh Yadav for 20 in the 50th.
Sammy finished with two sixes and five fours while Russell got two sixes and four fours during a fruitful partnership that also included some smart running by the pair.
The two built on the good work of Marlon Samuels, who steadied the innings with a 93-ball knock of 58 that included five fours and a six.
Samuels had a stand of 45 with left-hander Darren Bravo, who retired hurt on 26 with a hamstring injury that had curtailed his running between the wickets.
Samuels, who had smashed two consecutive fours off Mithun and later smashed Yadav for a six and two fours in an over, slowed down on Bravo´s departure and was out immediately after the powerplay was taken in the 33rd over.
Samuels tried to create space on the off side but was bowled by spinner Ravichandran Ashwin, who moved the ball away to uproot the off stump.
Denesh Ramdin (38) and Kieron Pollard (29) added 55 for the fourth wicket but were out before they could provide an impetus to the West Indies innings.
Earlier, openers Lendl Simmons and Danza Hyatt both fell to fine catches by wicketkeeper Parthiv Patel.
Simmons (1) was given out after a closer look by the third umpire as Patel took a low catch in front that seemed to have bounced. But television replays showed the wicketkeeper had got his hands under the ball just in time.
Hyatt grafted a slow 20 off 39 balls but was caught down the leg side just when he seemed to be opening up.
Patel also took a fine catch later in the day when he dived to his right to get rid of Ramdin off Yadav, who conceded 75 runs in nine overs.
Vinay Kumar was the pick of the bowlers with 2-39.
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