The Indians were skittled out for 105 runs in 25.3 overs in the 41-overs-a-side match, much less than their previous low of 191 in Port of Spain during the 2007 World Cup.
The stunning collapse was triggered by Taskin, who returned figures of 5/28, making it the best debut bowling performance by a Bangladesh player.
Skipper Suresh Raina's 23-ball 27, laced with three fours, was the best that an Indian batsman could manage under overcast conditions.
The resumption of play after three hours did not help matters for the visitors as Robin Uthappa (14) top-edged a skier to give Taskin, 19, his debut wicket in overcast conditions.
The lanky pacer continued to trouble the inexperienced Indian batsmen in conditions conducive to swing bowling. Cheteshwar Pujara (11) and Ambati Rayudu (1) were trapped lbw off Taskin.
