England 369 (Pope 91, Buttler 67, Broad 62, Burns 57, Roach 4-72) and 226 for 2 dec (Burns 90, Root 68*, Sibley 56) beat West Indies 197 (Holder 46, Broad 6-31) and 129 (Hope 31, Woakes 5-50, Broad 4-36) by 269 runs
Manchester: Stuart Broad's 500th Test wicket sent England on the way to completing a series victory over West Indies on the final day of the third Test at Emirates Old Trafford.
Broad had Kraigg Brathwaite lbw to become only the fourth pace bowler and second England player after James Anderson to reach the landmark, and would later take the final wicket to complete his third 10-wicket haul in Tests.
Brathwaite was the first man to fall, West Indies having resumed on 10-2 chasing 399 or, more likely, needing to bat out the day.
Chris Woakes claimed 5-50 as England dodged the showers to bowl West Indies out for 129, win by 269 runs and take the series 2-1.
After being beaten in the first Test in Southampton, England have come from behind to win a three-match series for the first time since 2008.
They also regain the Wisden Trophy and end the series third in the World Test Championship, behind India and Australia.
In a congested schedule, an entirely separate England squad play three one-day internationals against Ireland in the next week before the first of three Tests against Pakistan begins on 5 August.
West Indies, so competitive for much of the tour, remain without a series victory in the UK since 1988 and have now been beaten on seven consecutive trips to this country.
This was not only Broad's moment to join an elite club - only six other bowlers of any kind have reached 500 in Tests - but also further vindication after he so publicly voiced his displeasure at being left out of the first match of the series.
Since returning, he has taken 16 wickets at 10.93. In this match alone he picked up 10-67 to go with the 62 runs he scored in England's first innings.
To still be so determined at the age of 34 is typical of such a fierce competitor, whose 140-Test career has been characterised by spectacular spells and has taken in four Ashes wins.
Broad's 500th wicket came 40 minutes in, after a break for rain, when the hopping Brathwaite was hit dead in front by a full delivery.
He was congratulated with a hug from his great friend and new-ball partner Anderson, then raised the ball in the direction of the dressing room - the empty stadium denying the celebrations the achievement deserved.
Fittingly, Broad returned to seal victory. The first ball of a new spell was nothing but a long hop, but Jermaine Blackwood gloved a pull down the leg side to a diving Jos Buttler to make Broad only the seventh England player to take 10 wickets and score a half-century in a single Test.