With a modest, but vocal crowd cheering him on, Taylor snared five for 50 from 18.4 overs, as India were dismissed for 200 in their first innings just before stumps were drawn on an absorbing opening day on Friday.
Corey Collymore supported Taylor with two for 17 from 19 overs, and Dwayne Bravo collected two for 68 from 24 overs.
India captain Rahul Dravid hit 10 fours in the top score of 81 from 215 balls in close to six hours of batting for the visitors.
He added a vital 93 for the seventh wicket with Anil Kumble, who scored 45, that brought some respectability to India's total, after they had subsided to 91 for six just before tea.
Dravid was like the captain on the deck of the sinking Titanic as West Indies bowled with discipline, if not menace, to carve up India's batting on a pitch that offered bounce and movement.
It was a typically dogged innings from Dravid and he drew on all of his experience to hold firm for India as no other frontline batsman showed the level of adaptability that was required.
India had early knowledge that it was going to be a tough day for them when they slid to three runs for two wickets inside the first half-hour.
Openers Virender Sehwag and Wasim Jaffer, both thorns in the West Indies' side in the three previous Tests, failed to survive the opening burst from Taylor and new-ball partner Pedro Collins and were both dismissed cheaply.
Sehwag was caught at forward short leg off Collins for a duck in the first over of the match, and Taylor had Wasim Jaffer comprehensively beaten and bowled for one by a delivery moving back in the fourth over.
Dravid came to the wicket and with Venkatsai Laxman put their heads down to defy the West Indies attack and painstakingly carried India to 29 for two at lunch.
Laxman enjoyed a slice of fortune early in his innings when West Indies captain Brian Lara dropped him on five at second slip off Corey Collymore but the home team did not have to wait long to pouch him after the interval.
In the first over after lunch, Laxman was caught at gully for 18 off Dwayne Bravo slicing a drive.
Yuvraj Singh came to the wicket and with Dravid managed to slow down the rampaging Windies bowlers for close to half-an-hour, but Taylor had him lbw for 19 with a delivery that struck him a painful blow on the in-step to leave India on 58 for four.
Mohammed Kaif joined Dravid and tried to make headway, but he was caught at second slip off Taylor for 13 fending a short, rising ball.
Then Corey Collymore snared Mahendra Dhoni, caught at third slip for three to leave India in tatters.
Anil Kumble came to the crease and with Dravid carried India to tea on 102 for six, and continued to keep the West Indies' bowlers at bay.
But Bravo made the breakthrough when he bowled Kumble off the inside edge.
The Indian leg-spin bowler struck half-a-dozen boundaries from 101 balls in about two-and-three-quarter hours of batting.
His dismissal triggered a collapse that saw India lose their last four wickets, including Dravid, for 16 runs in 54 balls.
Collymore had Dravid caught behind, then Taylor bowled Sreesanth off the inside edge and wrapped up the innings when he had Munaf Patel caught behind fending a short, rising ball.
Both sides were unchanged from the previous Test that ended in a draw at Warner Park in Basseterre.
The four-Test series is still level at 0-0, with the first two Tests at the Antigua Recreation Ground and the Beausejour Cricket Ground also ending in draws.
India are seeking a win to clinch a series victory in the Caribbean for the first time in 35 years.
West Indies suffered an early setback in the match when Ramnaresh Sarwan was struck a painful blow below his left knee and had to be stretchered off the field.
He was taken to hospital for precautionary x-rays which revealed no fractures.