England's Stuart Broad (centre) celebrates the wicket of West Indies' Kemar Roach on the third day of the final Test
Broad's haul of 6-31 in 14 overs helped see the tourists dismissed for 197 - 172 runs behind England's first innings total of 369 that featured his dashing 62.
After the West Indies resumed on 137-6, Broad took four wickets for 11 runs in 22 balls.
But he came on after the West Indies had saved the follow-on.
England captain Joe Root, perhaps remembering how Shane Dowrich had struggled against the short ball in the hosts' 113-run win in the second Test, first deployed Jofra Archer and Chris Woakes on Sunday.
But Dowrich made a fine 37 before he was last man out to give Broad his 497th Test wicket.
West Indies, looking to retain the Wisden Trophy they won in the Caribbean last year, started the third day still needing 33 more runs to avoid the follow-on.
Jason Holder, the West Indies captain, was 24 not out and Dowrich unbeaten on 10.
The pair had shared an unbroken stand of 295, with Holder scoring a double century and Dowrich a hundred, during the West Indies' 381-run win in the first Test in their native Barbados last year.
With the hardness going out of the ball on Sunday, they both batted positively, with wicketkeeper Dowrich confidently pulling Woakes for four.
Holder, however, should have been out for 38 when, with West Indies still needing four more to make England bat again, clipped Woakes to midwicket, where a diving Ollie Pope held a brilliant catch.
But England's joy was cut short when a replay check by the umpires revealed Woakes had bowled a marginal no-ball.
Holder then ensured the follow-on was avoided by pulling Woakes for a resounding four.
But a stand of 68 ended when towering all-rounder Holder was lbw to Broad, bowling a full length, for 46.
Rahkeem Cornwall went the same way before Broad, controversially omitted from West Indies' four-wicket win in the first Test at Southampton, had Kemar Roach caught by first slip Root for a duck.
Dowrich cover-drove Broad for a superb back-foot four before he holed out to Woakes at mid-on.
The only pacemen to have taken more Test wickets than the 34-year-old Broad are Anderson (589) and the retired pair of Australia's Glenn McGrath (563) and West Indies' Courtney Walsh (519).
West Indies 1st Innings (overnight: 137-6)
K. Brathwaite c Root b Broad 1
J. Campbell c Burns b Archer 32
S. Hope c Buttler b Anderson 17
S. Brooks c Buttler b Anderson 4
R. Chase lbw b Broad 9
J. Blackwood b Woakes 26
J. Holder lbw b Broad 46
S. Dowrich c Woakes b Broad 37
R. Cornwall lbw b Broad 10
K. Roach c Root b Broad 0
S. Gabriel not out 0
Extras (b4, lb5, nb1, w5) 15
Total (all out, 65 overs, 321 mins) 197
Fall of wickets: 1-1 (Brathwaite), 2-44 (Campbell), 3-58 (Hope), 4-59 (Brooks), 5-73 (Chase), 6-110 (Blackwood), 7-178 (Holder), 8-188 (Cornwall), 9-188 (Cornwall), 10-197 (Dowrich)
Bowling: Anderson 16-5-28-2; Broad 14-4-31-6; Archer 17-1-72-1 (5w); Woakes 18-2-57-1 (1nb);
England: Rory Burns, Dom Sibley, Joe Root (capt), Ben Stokes, Ollie Pope, Jos Buttler (wkt), Chris Woakes, Dom Bess, Jofra Archer, Stuart Broad, James Anderson
Match position: England lead by 172 runs on first innings
Toss: West Indies
Umpires: Michael Gough (ENG), Richard Kettleborough (ENG)
TV umpire: Richard Illingworth (ENG)
Match referee: Chris Broad (ENG)