Tendulkar, the most successful batsman in One-day history, finished with an unbeaten 100 off 76 balls following a thrilling exhibition of power hitting by the hosts in the decisive match.
Indian captain Rahul Dravid and senior pro Sourav Ganguly joined the run feast with half-centuries after West Indian captain Brian Lara elected to field in good batting conditions.
Mahendra Dhoni hit an unbeaten 40 off 20 balls to help Tendulkar put on a blistering 75 runs from the last 40 deliveries.
Tendulkar, who was on 89 at the end of the 48th over, rotated the strike and helped himself to two boundaries to reach his first One-day century since making 141 against the West Indies in Kuala Lumpur in September.
Lara's men face a stiff target of 342 runs at 6.8 an over to draw the four-match series in their final international game before hosting the World Cup in March-April.
India did not look back after opener Robin Uthappa smashed 28 off 17 balls in a first-wicket stand of 47 with Ganguly in 6.3 overs.
Left-handed Ganguly then took over with an aggressive 68 that contained eight boundaries and a six to propel India to 148-1 by the 25th over.
The former India captain put on 101 for the second wicket with Dravid when he charged down the wicket against spinner Chris Gayle, missed the line and was easily stumped.
Dravid and Tendulkar continued the charge with their second consecutive half-centuries during a third-wicket stand of 118 that came off only 112 deliveries.
Dravid fell for 78 to set the stage for Tendulkar and Dhoni to send the tourists on a leather hunt.
India, still searching for a suitable World Cup combination, recalled Irfan Pathan for his first match since he was sent home from the tour of South Africa last month due to poor form.
India will play another four-match series against Sri Lanka next month before heading to the Caribbean on March 1.