Resuming on 329-3, in reply to Middlesex's 98 all out on day one, Tom Fell went early for 171.
But Kohler-Cadmore, 97 overnight, went on to finish on 130, with Ben Cox on 53, when the hosts declared on 431-5.
Middlesex were then bowled out for 205 after a 72-run last-wicket stand from Tim Murtagh and John Simpson (50 no).
Having initially looked comfortable second time around on 44-0, three wickets went down in eight balls when a double breakthrough for Ed Barnard got rid of ex-England openers Sam Robson and Nick Compton before Jack Shantry removed Paul Stirling.
After a brief break for rain, Dawid Malan and Neil Dexter briefly shored things up in a stand of 48, but Shantry made another breakthrough, West Indian signing Shannon Gabriel struck twice and another collapse, this time of six wickets for 31, was under way.
Having delayed the scheduled tea interval for half an hour, the last-wicket rearguard action between Simpson and Murtagh looked like extending the third day into a third session.
But, right on the stroke of tea, already relegated Worcestershire completed their season with victory when Murtagh was last out for 24 - the second of successive Middlesex run-outs.
Middlesex's defeat - only their second of the Championship season - could cost them second place to Nottinghamshire in the Division One table and their best finish since the introduction of two divisions in 2000.
It would mean an £81,000 disparity in prize money if third-placed Notts can pip them for second by beating relegation battlers Hampshire.
Worcs coach Steve Rhodes told BBC Hereford & Worcester:
"We're relegated but the players have tried so hard all season, they had a lot of pride and purpose and really showed what they can do.
"There have been a lot of frustrations during this year but we shan't get too down. We've now beaten three First Division teams by an innings.
"Tom Fell and Tom Kohler-Cadmore batted really well in this match. We have a lot of young players who are only going to get better and, I'm delighted to say, going to get better playing for us."
Middlesex coach Richard Scott told BBC London 94.9:
"To come here and lose to a side already relegated is disappointing.
"It will probably take a couple of weeks' reflection to find out what went wrong. But we have a lot to be proud of.
"We won seven games, did the double over Durham and Sussex, which is no mean feat, and there was the game at Lord's against Yorkshire, the highlight of the season."

Connie Jennings, 96, died following the crash on Friday morning, near Murthly on the A9. Ms Jennings was from West Yorkshire.
She was a passenger in a Mazda CX5 which collided with a D&E Coaches single-decker bus.
The driver of the car, a woman in her 60s, sustained less serious injuries. No one else was hurt in the crash.
Worcestershire youngster Tom Kohler-Cadmore made his maiden first-class century at New Road as Middlesex were beaten by an innings and 128 runs.
[NEXT_CONCEPT]
Police have released the name of a woman who died after a collision between a car and a bus in Perthshire.