At the Bridgestone Invitational, he became the 21st player to win a World Golf Championship and a major.
"This morning was a morning to score, for sure", added Fleetwood, who teed off on 10 and birdied 11, 13 and 16.
Rory McIlroy, playing in the final group with Thomas, said he was exhausted of finishing second this year. He made just a single bogey - at the sixth hole - and cruised to a closing 69 for a four-stroke victory.
His last nine holes saw two double bogeys, three bogeys, three birdies and just one par.
World number three Thomas has won eight times on the PGA Tour, but is still after his first World Golf Championships title.
Putnam closed with a 22-foot birdie putt from off the front of the green on the par-5 18th when a bogey would have been enough for the breakthrough victory at Montreux Golf and Country Club.
The only regret for Thomas was a mistake that didn't cost him as much as it could have.
It was a lot more hard, a lot firmer and I didn't quite hit it as well today but we just had such control of everything.
"We sat down and just said, what are we doing wrong?" Thomas followed suit, averaging a hefty 329.3 yards per measured drive (ranked 12th) and 75.0 percent of his greens (ranked T-2) to win the last playing of the event at Firestone by four strokes over Kyle Stanley. "I just played like crap".
Thomas said he told caddie Jimmy Johnson, "We can't see pin, hit pin".
He held steady on a day when the three players who started closest to the lead all fell apart.
"Oh, man, I'm going to miss this place, " he said. "And then I had some putts where, you know, I had some good looks at it to turn it around, build some momentum, I didn't make anything".
So ends a week that started strongly for the 14-time major champ.
"I needed to go get it today and I didn't do it". Both Thomas' dad, Mike, and his grandfather, Paul, were PGA of America pros - and Paul Thomas played in the 1960 PGA Championship at Firestone.
"It is the first time I have cried after winning a tournament".
Former World No.1 Day pulled within two shots of Thomas when he rattled off three straight birdies starting at the 10th hole, but a series of errant tee shots and poor recoveries resulted in back-to-back bogeys from the 13th.
"Things could have certainly gone better", Woods said.