"You want performances to lead to wins so to get to 500 on a day that we won a test match and a series feels very special," Broad said. "I feel so fresh and excited to play the game and I've done some technical work that makes me feel in great rhythm. Looking forward to getting back and playing against Pakistan (next week)."
Between Broad's milestones, Chris Woakes bowled 11 straight overs and took 5-50.
"Scoreboard pressure means so much to the bowling unit. We were relentless," Broad said.
Despite the bad ending, the West Indies deserved kudos for agreeing to travel to one of the world's worst pandemic hotspots and contributed to a gripping contest.
Cricket's first international action since March saw the West Indies win the first test and England the second. Both went down to the last day.
For this third test, England chose a four-man pace attack and the West Indies vulnerable lineup couldn't resist, falling for 197 and 129 against England's 369 and 226 declared.
For the first time since 1912 England pacers took 50 wickets in a three-match series.
Broad set up this victory on Sunday. He took four wickets to finish off the West Indies first innings, then the first two of the second innings in the evening to end West Indies' slim hopes of batting to win.
"Those big moments in series, he grabs them," captain Joe Root said. "He wants to take the ball when you're up against it."
The washout on Monday merely delayed England's march to victory, and the last day had an air of inevitability.
Broad's wait for his 500th was less than an hour, as he trapped West Indies opener Kraigg Brathwaite low on the back leg on 19. By a strange coincidence, Brathwaite was also Broad's fellow pacer James Anderson's 500th in 2017.
"How funny, that stat of Jimmy (Anderson) and I with Brathwaite," Broad said. "He said to me, 'You know who it's going to be, don't you?' That'll be a quiz question in a few years."
Shai Hope moved to a team-high 31, his best test score since January 2019, but gave away his wicket trying to pull Woakes.
Shamarh Brooks also gifted his to Woakes with a waft off his back foot that edged behind.
After lunch, Roston Chase hesitated twice running a single and was well short when Dom Bess, who was picked as a spinner but didn't bowl, brilliantly ran him out with a direct throw.
Woakes dismissed Jason Holder, Shane Dowrich and Rahkeem Cornwall with three consecutive leg befores, and Broad finished the series by dismissing Jermaine Backwood with the first ball of his new spell.
The West Indies didn't rotate its seamers like England did, but captain Holder, who bowled in all three tests, didn't think they tired.
"We won the first test with our best team. Trying to clinch the series, you try to put up your best team. You're trying to back the best team to do the job for you," Holder said. "I can't ask the bowlers to do much more."
The squad arrived in England seven weeks ago and spent all of it by necessity in a bio-secure bubble that Holder described as challenging.
"Mentally, some of the guys are a bit worn out," he said. "Same place, same rooms ... it could be this way for a little while. We've got to find ways to make it work."
Broad was rested for the first test and made his frustration with the decision public. He made his point with starring roles in both Manchester tests. But he suggested he won't be complaining again if he's rested during the three-test Pakistan series that starts next week on Wednesday.
"It's unrealistic to think that all of us will play all three tests against Pakistan with the workloads we've got," he said.
Most test wickets
800 - Muttiah Muralitharan, Sri Lanka (133 tests)
708 - Shane Warne, Australia (145)
619 - Anil Kumble, India (132)
589 - James Anderson, England (153)
563 - Glenn McGrath, Australia (124)
519 - Courtney Walsh, West Indies (132)
501 - Stuart Broad, England (140)
439 - Dale Steyn, South Africa (93)
434 - Kapil Dev, India (131)
433 - Rangana Herath, Sri Lanka (93)
431 - Sir Richard Hadlee, New Zealand (86)
