The Surrey opener, appearing in only his second Test match, defied a slight dislocation of the little finger on his left hand to reach 52 before being bowled by Shannon Gabriel. Alastair Cook fell for 23 after edging to wicket-keeper Shane Dowrich off the bowling off Jason Holder, who also had Tom Westley  caught behind after he should have been run out.
Captain Joe Root [45*] survived yet another drop on 10 and successfully challenged an lbw decision as he and Dawid Malan  steered England to stumps on 171-3 in their second innings.
"It has been quite a road to get here and I'm trying to embrace every opportunity and every innings that I play, never looking further forward than the next innings I go out to bat," Stoneman told Sky Sports.
"I was disappointed with my first Test innings but once I got through the first 20 balls of this innings you forget about the scrutiny that is going on behind the scenes and it was nice then to get in the contest and forget about everything else that does go on."
West Indies finished on Saturday at 329-5 after fine centuries from Kraigg Brathwaite and Shai Hope, but the latter could not prolong his stay at the crease this morning after nicking behind off James Anderson for a terrific 147 with the first ball of the day. The visitors lost two wickets in as many deliveries when Dowrich  edged to Root at second slip.
Moeen Ali inexplicably dropped Jermaine Blackwood on 4, but made no such mistake when dismissing skipper Holder  with a good take at long-off. Blackwood was then run out one short of his half-ton by a combination of Ben Stokes and Jonny Bairstow.
Stoneman missed the chance to end the innings with a spilled catch at short leg, but Gabriel's reprieve did not last long as he was trapped lbw by Stokes to leave West Indies all out for 427.