The big-hitting Trinidadian, who had gone 46 innings without a triple figure score, ended his drought by pummelling a boundary-filled 119 from 110 balls to put the Windies within sight of victory.
However, their target of 268 proved too much in the end and they were bowled out for 233 in the 45th over, as India won the series 4-1.
Manoj Tiwary had earlier put India on their way with a superb 104, a knock that hauled the hosts out of a hole in the first over where they rocked precariously at one run for two wickets.
Pacer Kemar Roach (2-46) removed opener Ajinkya Rahane and Parthiv Patel without scoring to the second and third balls of the innings, to leave the Windies on top.
However, Tiwary inspired two partnerships to instigate India’s recovery, putting on 83 for the third wicket with captain Gautam Gambhir (31) and a further 117 for the fourth wicket with Virat Kohli whose 80 required just 85 balls.
Seamers Abhimanyu Mithun (2-32) and Irfan Pathan (2-42) then wiped out the West Indies top order, to lay waste the innings at 36 for five in the 10th over.
In-form opener Lendl Simmons fell to the first ball of the innings, lbw on the backfoot to left-armer Pathan, and his opening partner Kieran Powell stroked three fours in 15 before also playing back to Pathan and going bowled off the inside edge at 23 for two in the fifth over.
Marlon Samuels was controversially adjudged caught at the wicket for six off Mithun, a decision given by umpire Sudhir Asnani even before the bowler had appealed.
When debutant Jason Mohammed played across to Mithun and was lbw for two in the 10th over, West Indies needed something special and they got it from Pollard.
The right-hander first added 42 off 37 balls for the fifth wicket with Denesh Ramdin (14) but when the wicketkeeper became the first of left-arm spinner Ravindra Jadeja’s (3-62) three wickets starting in the 16th over, Pollard took matters into his own hands.
Striking the ball cleanly and with astonishing ease, he counted four fours and 10 massive sixes, to leave the MA Chidambaram Stadium in awe.
He reached his half-century off 43 balls by hitting Jadeja straight for his fourth six and then brought up his first ever ODI century with a four in fortuitous circumstances, when Kohli dropped a simple chance at long-off leg-spinner Rahul Sharrma, and the ball crossed the ropes.
Along the way, Pollard shared 89 for the sixth wicket with all-rounder Andre Russell who belted five fours and three sixes in a marvellous 42-ball 53.
Together, they threatened to uncork a Windies win but Russell was eventually run out in the 29th over by a direct hit from Gambhir at short third man, sparking a decline which saw the last five wickets tumble for 66 runs.
Pollard was last out, drilling off-spinner Suresh Raina down the throat of Rahane at long-off, to end a scintillating innings.
Earlier, it was Tiwary who put India back on course after Roach’s two early strikes. Rahane was lbw on the back foot to one that kept low while Patel played on next ball.
The right-handed Tiwary then stroked 10 fours and a six off 126 balls with support from Kohli who five fours.