Tendulkar missed out on a potential 100th international century, but his innings put India in a winning position on the fourth day at the Ferozeshah Kotla Stadium.
He added 67 for the third wicket with Rahul Dravid (31) and 71 for the next with VVS Laxman (58 not out) as India cruised to the win with almost five sessions to spare.
“That was a big lead, we all felt we did not bat the way we should have in the first innings,” MS Dhoni, the India captain, said of chasing down their target of 276. “It was not an easy wicket to score, you had to be aware of the ball that kept low.”
India’s famed batting line-up, which had folded for only 209 in the first innings, made few mistakes the second time around and also buried fears of low bounce on a pitch which did not see huge scores.
“When you play against a top team, you want to create the opportunity to win which we did that in the first innings,” Darren Sammy, the West Indies captain, said. “We did not bat well in the second but believe we can win matches here.”
Yuvraj Singh (18) was bowled by Sammy with just one run needed for victory, leaving Dhoni as the other not out batsman without scoring a run.
Tendulkar, who resumed on 33, closed in on his milestone but was trapped lbw by leg-spinner Devendra Bishoo when trying to pull a short-pitched delivery. He hit 10 fours in his 148-ball innings.
A crowd of more than 10,000 had turned up at the ground to watch Tendulkar get another three-figure mark but went back disappointed as the Mumbai batsman failed to do so.
Tendulkar, who became the first batsman to reach 15,000 Test runs on Tuesday, has been on 99 centuries since the Cricket World Cup in March-April this year when he struck tons against England and South Africa.
Tendulkar smashed two fours each off overs from pace bowlers Darren Sammy and Ravi Rampaul to raise hopes of ensuring a win as well as reaching his personal target.
Laxman, who had started with a couple of trademark shots off the leg to pace bowler Fidel Edwards early in his innings, struck six fours off 105 balls.
The wristy Hyderabad batsman ensured India returned to winning ways in style after a forgettable previous Test series which they lost 4-0 in England.
Earlier, overnight batsman Dravid was out for 31, adding only one run to his overnight score.
Fidel Edwards, the pace bowler, bowled a beautiful incoming delivery that went between bat and pad. Dravid batted for a total of 154 minutes, hitting only three fours off 101 balls.
The West Indies, who had won a previous two-Test series in Bangladesh by a 1-0 margin, had a comfortable 95-run first innings lead but failed to drive home the advantage when India bowled the visitors out for only 180 in the second innings.
The next Test will be held in Kolkata from November 14 and the final game in Mumbai from November 22.
The Tests will be followed by a series of five one-day internationals.