Fast bowler Mark Wood polished off the tail with a spell of 5-9 in six overs to finish with 5-40 in 14 overs.
West Indies opener Mikyle Louis, whose 57 was his maiden Test fifty and Kavem Hodge (55) offered some resistance but the next highest score in the innings was 12 -- a total shared by Alick Athanaze, Jason Holder and extras.
England opening batsman Zak Crawley had earlier left Edgbaston for a scan after suffering a blow to his right index finger while dropping a slip catch in Sunday's first session, with captain Ben Stokes taking his place at the top of the order for the run chase.
England have already won this three-match series at 2-0 up after an innings and 114-run win at Lord's was followed by a 241-run win at Trent Bridge.
