The England captain needed only 24 deliveries on Sunday to reach his half-century. He finished on 57 off 28 balls and got the winning runs with a six off Kraigg Brathwaite. Ben Duckett contributed a 16-ball 25.
The opening pair scored at a run rate of almost 12 to hit 0-87 in 7.2 overs in England's second innings.
Regular opener Zak Crawley fractured his little finger in the field, giving Stokes the opportunity to promote himself to opener and entertain the Edgbaston crowd.
West Indies resumed on Sunday on 2-33 but collapsed against Wood. He took his wickets in a ferocious spell after lunch, dismissing Josh Da Silva, Alzarri Joseph, Kavem Hodge, Jayden Seales and Shamar Joseph in the space of 21 dramatic deliveries.
Wood intimidated the tourists with bumpers, threatened their outside edges with reverse swing and blitzed the stumps when he went full and fast.
Mark Wood wrecked the Windies batting line up. (AP PHOTO)
"It was an amazing spell. He's got the heart of a lion and that's exactly what you want as a captain," Stokes said.
By the time Wood was done the tourists had slumped from 5-156 to 175 all out, leaving England chasing just 82 to win.
Gus Atkinson claimed 2-28 and Stokes also contributed with the ball by claiming West Indies top-scorer Mikyle Louis for 57. Hodge was caught behind against Wood for 55.
Stokes shaved four deliveries off Ian Botham's 43-year-old record of 28 balls for England's fastest ever Test half-century.
"I'm pretty chuffed to go past Beefy," Stokes said. "A bottle of champagne would be appreciated."
It was Test cricket's third-fastest 50 overall.
Only Pakistan's Misbah-ul-Haq, who reached the same landmark in just 21 deliveries against Australia in Abu Dhabi in 2014, and David Warner, who did it in 23 for Australia against Pakistan in Sydney three years later, are ahead of Stokes in the all-time list.
Seamer Gus Atkinson was England's player of the series after taking 22 wickets overall. Jayden Seales, who took 13 wickets overall, was West Indies' player of the series.
England won the first Test at Lord's by an innings and 114 runs, and the second test at Trent Bridge by 241 runs.
