Praveen Kumar was the most successful Indian bowler with three for 37 from 10 overs, and leg-spinner Amit Mishra captured two for 56 from 10 overs, as the visitors again kept the West Indies batting in check on another hard, true Vivian Richards Cricket Ground pitch.
Pollard smashed six fours and two sixes in the top score of 70 from 72 balls to spark a West Indies revival, after they stumbled to 103 for five in the 27th over.
Simmons supported with 67 from 78 balls, Carlton Baugh Jr made 39, and Andre Russell, the West Indies batting hero from the previous match, added 25.
The new ball pair of Kumar and Ishant Sharma, one of the three changes to India's line-up for the match, struck early on, leaving the hosts on 12 for two.
Sharma had opener Danza Hyatt caught at backward point for one in the second over, and Kumar had Ramnaresh Sarwan caught in the same position for the same score in the fifth over.
The Indians met resistance in the form of a 53-run stand between left-hander Darren Bravo and Simmons before Mishra triggered another mini-crisis, West Indies losing the pair, as well as Marlon Samuels for 38 in the space of 65 deliveries.
The visitors were again put on the back-foot, when Pollard and Baugh added 96 - largely untroubled - for the sixth wicket to move West Indies in the right direction.
But off-spinner Ravichandran Ashwin had Pollard caught at long-on in the 45th over - the second over of the Batting Power Play - before Baugh and Russell continued West Indies attacking intent, briskly putting on 41 for the seventh wicket.
Kumar returned for his final spell, and removed Baugh and Russell off successive balls in his final over - the penultimate of the innings - but West Indies would have felt reasonably content with their final total.
India made three changes, bringing Sharma, Ashwin, and left-handed batsman Manoj Tiwary, in to replace Munaf Patel, Harbhajan Singh, and Shikhar Dhawan.
West Indies made two changes, swapping Bravo and leg-spinner Anthony Martin for Kirk Edwards and Devendra Bishoo respectively.
The Indians hold an unbeatable 3-0 lead in the five-match series.
The world champions are looking to close in on a clean sweep in an ODI series for the first time on Caribbean soil, and can take comfort in the knowledge that West Indies have never won any of the five ODIs they have played at the VRCG.
