England began the unenviable job of batting their way back into the second Test after the West Indies built a 119-run first-innings lead.
England bowled the hosts out for 306 in Antigua, taking their four remaining wickets for 34 runs on the third morning.
Darren Bravo was last man out for exactly 50, the West Indies' slowest ever half-century having taken 215 balls.
Resuming on 272 for six, Bravo and Jason Holder continued the belligerence they had shown on the second evening, taking half-an-hour to add just nine to the total.
James Anderson made the breakthrough, finding Holder's outside edge to leave a simple take for Jonny Bairstow behind the stumps.
Roach was less patient, throwing the bat at Anderson and sending a high catch whizzing to Ben Stokes at second slip.
That brought Joseph to the crease, welcomed by a lengthy round of applause by the predominantly English crowd and generous claps from the fielding side.
He added seven before poking Stokes' first ball low to third slip, where Burns held on well.
Bravo was tempted out of his shell by the introduction of Moeen, launching a six after 174 balls with no boundaries, and found himself stumped off the spinner immediately after reaching his 50.
