Tendulkar, the most successful batsman in one-day history, reached his hundred off the last ball of the innings as India piled up 341-3 and then bowled out the West Indians for 181 in 41.4 overs in Vadodara Wednesday.
Marlon Samuels top-scored for the tourists with 55 and Denesh Ramdin made 40, but the remaining batsmen showed no signs of being able to chase down a stiff target of 6.8 runs an over.
The tourists were reduced to 83-5, including the unfortunate run out of captain Brian Lara, who backed up too far at the non-striker's end and was out after a Samuels straight drive deflected off the bowler on to the stumps.
Ajit Agarkar and Anil Kumble grabbed two wickets each to hand the West Indies a morale-sapping defeat in their final one-dayer before they host the World Cup starting in March.
India will play another four-match series against Sri Lanka at home next month before heading to the Caribbean on March 1.
Tendulkar 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 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 also helped himself to two boundaries to reach his first one-day century since making 141 against the West Indies in Malaysia in September.
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 Indian captain had 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 during a third-wicket stand of 118 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.
The all-rounder did not get a chance to bat and finished with one for 43 from seven overs with the ball.