The Sheffield pair became the first brothers to win the team event, while Matt became the first player in more than two years to win back-to-back events on the PGA Tour and the first Englishman to win three times in the same American season.
His superb 35-yard bunker shot at the par-five last left his younger sibling with a tap-in to post 31 under and avoid a three-way play-off on Sunday (Monday AEST).
With the victory Alex, who holed the winning putt in the last-round foursomes, earned a PGA Tour card through 2028 with exemptions to the next four Signature Events, next month's US PGA Championship and the 2027 Players Championship.
The pair had begun the day with a four-stroke lead but a bogey on the 14th meant that had been whittled away after Matt had driven behind a tree and Alex's recovery rebounded off another resulting in a double bogey on the 12th.
Matt, who won last week's RBC Heritage, was struggling despite being the more experienced player and when Alex hit his tee shot to 14 feet at the difficult par-three 17th his brother mis-hit the birdie attempt.
Norwegians Kristoffer Reitan and Kris Ventura and American pair Alex Smalley and Hayden Springer were already in the clubhouse on 30 under, but Matt redeemed himself down the last with a superb sand save to set up the crucial, career-changing birdie for his brother.
"It was a struggle. I was doing absolute (sic) zero to help him apart from the putt I made on 15. I wasn't providing much support but he (Alex) was fantastic on the back nine," said world No.3 Matt.
Alex, ranked 141st in the world, has until 5pm local time on Monday to officially join the PGA Tour to be eligible for the $US20 million ($A28 million) Cadillac Championship which starts on Thursday at US president Donald Trump's Doral resort in Florida.
"It won't sink in – I've got a flight booked for Turkey tonight (as he was scheduled to compete in the Turkish Airlines Open on the DP World Tour), Alex added.
"It's amazing to be here with him (Matt), mum and dad. It's as good as it gets."
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