England had declared their second innings at 129-3 in the first session in Manchester after sizzling all-rounder Stokes smashed 78 off 57 deliveries, setting West Indies a target of 312 with 85 overs left in the day.
England’s fast bowlers Stuart Broad and Chris Woakes struck early to reduce the visitors to 37-4 but met stiff resistance in the form of Shamarh Brooks and Jermaine Blackwood, who hit half centuries and added 100 runs for the fifth wicket.
But Stokes dismissed Blackwood (55) on the stroke of tea while Sam Curran had Brooks trapped leg before wicket for 62.
Skipper Jason Holder frustrated the English bowlers as he dug himself in before being bowled by Dom Bess for 35 to open up the tail.
“I’m a little disappointed with the way we batted,” Holder told the BBC. “Yesterday’s evening batting performance probably really set us back.
“If we were batting into today’s play we would have been best set to save the game or even give ourselves a chance to win.”
Earlier, England resumed on their overnight score of 37-2 and Stokes got straight into the action, looking to cart the bowlers all around the empty stadium to bring up his half century in only 36 balls.
Stokes, who scored 176 in the first innings, was unbeaten on 78 off 57 deliveries, which included three sixes, when England declared.
“Ben keeps developing his game and improving all the time. Credit to him, he really has taken every opportunity to make himself a better player,” England captain Joe Root said.
“Throughout the game you’ve seen how destructive he can be when he needs to be and also when he needs to bat time and play to the situation, he can do that too.”
There was concern, however, that Stokes had injured himself when he failed to complete an over towards the end of the game although the ‘Man of the Match’ brushed it aside.
“I’m fine, the body started to get quite stiff,” Stokes said. “I said to Broady that I was feeling quite stiff, what do you reckon, and he said stop.
“I’ll give everything to the team, whatever’s asked of me. We’ve found a method within our attack to be aggressive when things aren’t happening.”
The series is being played behind closed doors due to the COVID-19 pandemic. The third Test which begins on Friday will also be played in Manchester.