Stokes hit the quickest test half century by an English batsman, and was unbeaten on 55 off 28 balls as England took 7.2 overs to reach their victory target of 82.
Wood claimed five wickets in four overs - three in a single over - to skittle out West Indies for 175 in their second innings.
With Zak Crawley having hurt his hand, it was the perfect stage for Stokes to promote himself up the order and the skipper wasted no time in thrashing the bowling to all corners of the ground.
Ben Duckett played the supporting role, scoring 25 runs off 16 balls.
England matched their own record for being the fastest team to reach 50 runs in a test, achieved in 4.2 overs, while Stokes' 50 off 24 balls bettered Ian Botham’s 28-ball half-century in India in 1981.
"Pretty cool to go past Beefy (Botham) with that one. A bottle of champagne from him would be better appreciated than a well done message," said Stokes.
"I don't think we must under-estimate this series. We were 50-5 at one stage but fought back to win it inside three days," he added.
Earlier, Wood produced a brilliant burst of fast bowling after lunch to run through the tourists’ tail, with his five wickets costing only seven runs.
Windies were always up against it with a 94-run first innings-deficit but looked to be putting up a fight in the morning session with half centuries from Mikyle Louis and Kavem Hodge.
They were never able to put together any meaningful partnerships, however, as England took three wickets before lunch and Wood ripped through the tail to finish with figures of 5-40 in 14 overs.
Louis and Alick Athanaze had resumed with the Windies on 33-2, and the 23-year-old Louis reached his 50 with an impressive six over long on before he was caught at slip by Crawley off Stokes.
Hodge raced to his half century in 56 balls as he looked to put pressure on the bowlers but was Wood’s second victim as he got a healthy edge and was caught behind.
Wood had removed Joshua da Silva lbw and after Hodge went for 55, bowled Alzarri Joseph (2) and Jayden Seales (0) before finishing off the innings when Harry Brook caught Shamar Joseph at second slip.
England move onto a three-test home series against Sri Lanka, starting on August 21st, while the West Indies return home for a two-test series against South Africa beginning next week.
