Pope remained unbeaten on 91, while Buttler was not out on 56 as England ended the day on 258 for 4.
Pope and Buttler added a century stand together.
Pope survived a couple of close chances, but went on then to make his half-century.a
Burns got to his half-century and looked set for a big one, but once again Roston Chase had him cut a fuller one that flew to slip. Cornwall took a sharp catch to send him back for 57.
Roach then set up Stokes with two bouncers followed by a fuller delivery that knocked his stumps out after Lunch.
Just on the brink of Lunch, Joe Root, in the attempt of scampering through for a quick single, fell short as Roston Chase's direct hit knocked the bails out with the skipper falling short.
Rory Burns and Joe Root staged a resilient partnership thereafter with the West Indies quicks getting some movement.
Kemar Roach struck in the first over of the Test, trapping Dom Sibley plumb in front for a duck.
England's players wear red caps for Ruth Strauss Foundation Day prior to the start of the deciding Test.