Pollard's (119) blistering 110-ball knock took his team close to the 268-run victory target but apart from Andre Russell (53), none of his batting colleagues could offer much support as West Indies folded for 233 in 44.1 overs.
With only number 11 batsman Anthony Martin to give him company and still 35 runs required off the last six overs, Pollard tried to hit Suresh Raina for his 11th six but found Ajinkya Rahane in the deep.
India won the five-match series 4-1.
West Indies had lost opener Lendl Simmons to the first ball of their innings and slumped to 78 for five before an 89-run stand between Pollard and Russell brought them back in the match.
Pollard tried to hit his way out of trouble but wickets continued to tumble around him. He was fortunate to get his maiden century which came when Virat Kohli dropped him for a four in the 43rd over.
Earlier, Manoj Tiwary (104) struck his maiden century before retiring hurt with cramps while Kohli (80) became the highest ODI run-getter in 2011 as India posted a challenging 267 for six at M.A.Chidambaram Stadium's low and slow track.
Gautam Gambhir, leading in absence of Virender Sehwag, won the toss and opted to bat first but the hosts were rattled early, losing two wickets in the first three deliveries.
Kemar Roach's second delivery kept low and hit Rahane's pad and next-man-in Parthiv Patel dragged the next delivery on to his stumps to become the second Indian batsman out for a first-ball duck.
Tiwary, playing his first match of the series, not only denied Roach a hat-trick but also decided to make the most of the opportunity that came his way.
The right-handed batsman added 83 runs with Gambhir (31) to steady the innings and shared a more fluent 117-run partnership with Kohli to lay the foundation for a big total.
Tiwary hit spinner Sunil Narine for a four to reach the 100-mark but the humidity took its toll on his body and the batsman limped off the ground after taking a single off the next delivery.
His 126-ball included 10 fours and a six.
Kohli, however, did not get his century, and became Anthony Martin's second victim after a smooth 85-ball knock.
