Broad started day five needing just one wicket to become the seventh player to reach the landmark and achieved the feat by removing Kraigg Brathwaite, the same batsman James Anderson dismissed to join the 500 club in 2017.
Pace great Broad, dropped for the first Test in Southampton, then took the series-clinching wicket to finish with 4-36 after the brilliant Woakes claimed 5-50 to bowl the tourists out for only 129.
Broad, who took match figures of 10-67 and smashed a half-century, and Woakes sat out a first match of the series that the Windies won at the Rose Bowl, but showed what England were missing in Manchester.
The Windies head home on Wednesday, still without a Test series win in England since 1988 after losing a contest to be renamed the Richards-Botham Trophy when they next do battle.
Shai Hope and Brathwaite got the Windies off to an encouraging start after resuming on 10-2 following a day-four washout, but Broad ended a 39-run stand by trapping the opener bang in front to join the 500 club after a rain delay.
Broad remained in the thick of the action, running in from mid-off to catch Hope (31) and Sharmah Brooks edged behind (22) to become Woakes’ second victim.
Rain ensured early lunch was taken with the Windies in deep trouble on 84-5 and Dom Bess – who did not bowl a ball in the match – ran Roston Chase out before another shower took the players off again.
Captain Jason Holder, Shane Dowrich – who took a nasty blow to the face while wicketkeeper – and Rahkeem Cornwall were snared lbw in a devastating spell from Woakes.
Broad fittingly finished it off, Jos Buttler taking an excellent catch down the leg side to dismiss Jermaine Blackwood and give England’s man of the moment 10 wickets in a Test for the third time.
Broad goes from seething in Southampton to main man in Manchester
Broad was furious after being left out for the first match of the series and could only watch on as the Windies took a 1-0 lead in Southampton.
The paceman has let his performances do the talking in the remainder of the series, playing a major part in England’s turnaround with bat and ball.
His dismissal of Brathwaite saw him become the fourth seamer – and the second-youngest bowler behind Muttiah Muralitharan – to claim 500 Test scalps and he put the icing on the cake by taking the last wicket with his first ball of a new spell.
Hope fails to live up to expectations
It was an all too familiar story for Hope on the last day of what has been a poor tour for a batsman who has not shown what he is capable of.
Hope played positively as he made his highest score of the series, hitting six boundaries before throwing his wicket away attempting to dispatch Woakes for a seventh.
The number three heads home without making a half-century three years after making a century in both innings at Headingley. He has not reached three figures in a Test since that famous win in Leeds.
Woakes makes his mark
Woakes was also omitted for the defeat at the Rose Bowl and has responded impressively.
He took five wickets in the second Test and added another in the first innings this week before ending the series on a high note.
The all-rounder was on the money on the final day, rewarded for consistently bowling on a probing line and length with a fourth five-wicket Test haul.
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