Pollard smashed 10 sixes and four boundaries in his 110-ball knock before the tourists were bowled out for 233 in reply to India's 267-6 in the day-night match at the Chidambaram stadium.
Pollard was last man out, caught in the deep off Suresh Raina, to deny his team a win in the last match of the Indian tour, where the West Indies also lost the Test series 2-0.
The West Indies were reduced to 78-5 by the 16th over before Pollard and Andre Russell turned the game around by smashing 89 off 79 balls for the sixth wicket.
The pair pounded the Indian bowling with a flurry of fours and sixes before the hosts earned a lucky break when Russell was run out by a direct throw from Gambhir.
Russell hit 53 off 42 balls with five boundaries and three sixes.
Three more wickets fell in quick succession to leave the West Indies tottering at 213-9, but Pollard reached his maiden one-day century in the company of last man Anthony Martin.
Earlier, Manoj Tiwary smashed 104 as India recovered from a shaky start to post a challenging total.
The 26-year-old from Bengal, making his first appearance in the series, registered his first international century after India had lost two wickets in the first over of the innings.
Tiwary put on 83 for the third wicket with stand-in captain Gautam Gambhir and 117 for the fourth with Virat Kohli before retiring hurt in the 38th over due to cramps.
Kohli went on to make 80 off 85 balls.
India, already assured of a series win, rested three players, including skipper Virender Sehwag, who had compiled a world record one-day score of 219 in the previous match in Indore.
Sehwag, Ravichandran Ashwin and Vinay Kumar, who leave for Australia on Monday for the Test series starting later this month, made way for Tiwary, Irfan Pathan and Ajinkya Rahane.
The right-handed Tiwary, who had scored only 61 runs in five previous one-day internationals, seized his opportunity, hitting 10 boundaries and a six in his 126-ball knock.
Tiwary prevented a hat-trick when he came to the crease in the first over after Kemar Roach had trapped Rahane leg-before with his second delivery and bowled Parthiv Patel with his third.