With the best final round by a winner in the tournament's history, Cantlay finished at 19-under 269, while Australian Scott continued his good form with a 68 at Muirfield Village.
The 27-year-old Cantlay arrived at the Memorial brimming with confidence after a tie for third at the PGA Championship two weeks ago.
He surged into contention on Sunday with five birdies on the front nine and added three more coming home, almost making eagle at the par-five 15th before tapping in for par.
He will leave with sights set on the next major, the U.S. Open at Pebble Beach in his native California next week.
"I really like major championship golf," he said.
"I feel like it suits my game. I feel like the golf courses, as far as I'm concerned, the rough can't be long enough, the fairways can't be narrow enough, the greens can't be fast enough. I love golf like that."
Cantlay, 27, has a serious demeanour borne of some hardships but he was able to crack a smile for tournament host Jack Nicklaus, who was waiting to greet the winner next to the 18th green.
They both live in the same community in south Florida, and Nicklaus has been a mentor to Cantlay for the past couple of years.
"The relationship I have with Mr. Nicklaus is extremely special to me and I appreciate all the time he's spent giving me advice and trying to help me in any way that he can," said Cantlay.
"He said just to relax and have fun and look around and see all the people having fun and try to smile and just have a good time with it.
"Hearing it from someone like Jack gives it a little more weight, a lot more weight."
Cantlay had to deal with a potentially career-ending back injury, virtually sidelined for three years from 2013 with a stress fracture.
In 2016, he witnessed the death of a close friend who was struck by a vehicle as the two were walking down a street in Newport Beach, California.
"I get asked questions a lot about how the difficulties with my friend Chris dying and being out so long with my back, how it affects me now (and) I'm definitely a different person than I was before I went through any of those troubles," he said.
"I can remember feeling happy-go-lucky, like everything is going to go good ... and during that time I realised that you can put in a lot of good work, and good things still might not necessarily happen."
(Reporting by Andrew Both in Cary, North Carolina, editing by Ed Osmond)
