Martin was ably assisted by seamer Andre Russell (3-16) and captain Darren Sammy (2-43) as India crumbled to 146 all out in pursuit of West Indies' 249-8 off 50 overs.
The hosts' total had earlier been built around opener Lendl Simmons, who scored 67 off 78 balls, and Kieron Pollard's well-crafted 70 off 72 deliveries.
Simmons anchored the top order while fellow Trinidadian Pollard guided the hosts after a middle-order collapse.
Seamer Praveen Kumar led the visitors with 3-37 while leg-spinner Amir Mishra claimed 2-56.
Sammy was delighted that his team could finally post a win in the series to reduce the deficit to 3-1.
"We did a lot of the things better in this game," he said. "Throughout the series, we've been improving. As long as we keep improving, I'm happy. We've still got a young team and we're still trying to find that winning mindset and today it was really good to see the guys putting out a keen effort."
Indian captain Suresh Raina was critical of his batsmen.
"We didn't bat well, to be honest. Our shot selection was really wrong," he said. "We kept losing the shape. We kept losing wickets and we didn't have partnerships in between."
India's new ball pair of Kumar and Ishant Sharma made early inroads after captain Suresh Raina won the toss for the fourth time and again sent the hosts in.
Sharma struck first when Danza Hyatt (1) spooned a catch to Manoj Tiwarty at backward point off the shoulder of the bat.
West Indies slumped to 12-2 when Ramnaresh Sarwan (1) slapped Kumar to the same fielder.
Simmons and Darren Bravo rebuilt in a stand of 53 for the third wicket before Mishra made his mark.
Bravo compiled 15 off 36 balls before he chipped an on-drive to deep midwicket where Tiwary hauled in his third catch.
Marlon Samuels (8) was also a Mishra victim, leg before wicket to a googly.
Simmons struck three sixes and three fours in notching his sixth half-century in his last eight one-day innings. But Tiwary's direct hit from short midwicket ran out the right-hander and left the West Indies reeling at 103-5 in the 27th over.
Pollard and wicket-keeper Carlton Baugh ensured the innings reached respectability, adding 96 off 107 balls for the seventh wicket.
Pollard dominated, lashing six fours and two sixes in his fourth one-day 50, while Baugh notched 39 off 57 balls.
Pollard holed out to long-off in the batting powerplay, but Andre Russell (25 of 14 balls) kept the momentum towards the end.
Kumar claimed both Baugh and Russell in the penultimate over to end with the best figures.
India's reply never managed to find any momentum once Sammy removed both openers with his medium pace.
Manoj Tiwary, in his first match of the series, pushed tentatively outside off and feathered a catch to wicket-keeper Carlton Baugh.
Parthiv Patel struck three fours in 26 off 32 balls before Sammy grasped a stunning one-handed return catch to end his resistance at 41-2.
Russell removed Subramaniam Badrinath to a fine Baugh catch behind as India slipped further to 62-3.
Martin tightened the home team's grip by removing Virat Kohli (21), captain Suresh Raina (10) and the in-form Rohit Sharma (39).
Kohli was beaten in flight and stumped by Baugh while Raina played an expansive stroke and hauled a catch to midwicket.
Lendl Simmons' part-time medium pace accounted for Yusuf Pathan (1) before Sharma top-edged a slog at Martin at 124-7.
Russell ensured there would be no fightback, dismissing Praveen Kumar and Ravichandran Ashwin.
Martin was left to deliver the final rites, Baugh claiming his fourth scalp with a swift stumping of Ishant Sharma.
