Spinner Dom Bess took two of the four wickets to fall on the day, carrying more than his share in the most batsman-friendly conditions of the match to date.
The West Indies began on 57 for one, 147 short of England's mark, with Kraigg Brathwaite and Shai Hope chipping another 42 off the deficit in the first hour of play.
There were just a couple of boundaries in that period, the second of which flew a yard over gully as Jofra Archer thumped the shoulder of Hope's bat. Brathwaite was more comfortable, doing most of the scoring without exposing himself to undue risk.
Hope earned a reprieve just before the drinks break, an Archer lbw chalked off after the paceman overstepped for a no-ball. England were not made to pay for that error, with Hope aiming a big drive at Bess just a few deliveries later and sending a sharp slip catch in Stokes' direction.
The arrival of Shamarh Brooks lifted the run-rate, with the new batsman helping himself as Archer and Bess offered some loose fare.
Brathwaite was looking resolute at the other end, converting his overnight 20 into the first-half century of the match from 113 balls.
It was also his first Test 50 since July 2018 but his hopes of progressing towards three figures ended when Stokes pushed him on the back foot and rapped him high on the knee roll. He was given out for 65 by Richard Kettleborough and when he called for the review the dismissal was upheld on two counts of 'umpire's call'.
While that was enough to justify the decision, the West Indies would be forgiven for harbouring frustration at the number of tight calls that have gone against them in this match – the first since the International Cricket Council relaxed its rules on the use of 'home' officials.
An inside edge off Chase's bat took the score within 50 of England by lunch.
The brakes were successfully applied at the start of the afternoon session as Anderson and Bess built up pressure with dot balls. It took nine overs to build to a head but when it did Brooks wafted at Anderson and nicked to Jos Buttler for a useful 39.
England kept the squeeze on and it did not take long to exhaust Jermaine Blackwood's notoriously small reserves of patience. The number six swung hard at Bess as he wheeled away, hacking to Anderson at mid-off to make it 186 for five.
Chase slowed to a crawl to reach 27 not out in 115 deliveries but Dowrich kept things moving, going after Bess with three boundaries down the ground, to begin the job of taking the game away.