The result was a 6-under 64 for the 34-year-old American, who vaulted into a tie for third place with Thorbjorn Olesen at 10 under.
Spieth made a run at completing the career grand slam in just one year in 2015, when he won the Masters and U.S. Open before finishing T4 at The Open Championship and second in the PGA Championship.
After a bogey from the trees at No. 3, Thomas went at a back pin on the tough fourth hole and the ball bounded over the green in thick rough.
"I take a lot of pride in how I played today", Thomas told reporters.
"My goal today I was trying to get to 18 under, because I knew if I got to that I didn't think anyone would catch me". That allowed him to regain the lead over Anthony Quayle, who had made eagle on the same hole moments earlier and closed with a 63. "The golf course is playing very soft, very receptive and when you're able to hit five-irons and they only roll out about a foot, the guys are going to put up good scores". Playing two groups in front of Perry, Short got within two shots with three holes to go, but Perry made a birdie putt at 16 for a three-shot cushion. Obviously I have a day left, but I played three really good days of golf.
The win is the third for Thomas in the 2018 season, but his first since the Honda Classic in February. "This is my first PGA Tour win with them here, so it's pretty cool", the 25-year-old said after joining Dustin Johnson and Bubba Watson as three-times winners on the tour this year. I never have gotten like that on the golf course before.
The Thomas family already has a history at Firestone Country Club. "I can't really put it into words, honestly", he said.
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"I was just signing my card there and realized I hadn't had a five", Fleetwood said.
He said the victory was particularly special given his grandfather, who played in the 1960 US PGA Championship at Firestone, was in the gallery.
Rounding out the Australian contingent at Firestone was Adam Scott, who birdied the final hole but a 74 left the 2011 victor at four over. He'd just won the final installment of the WGC-Bridgestone Invitational at Firestone surrounded by family.
He started his comeback this year ranked outside the top 500 in the world, moved to 50th - and secured his berth in this week's elite event - with his share of sixth place at the Open Championship.
Putnam earned $$612,000, a two-year tour exemption and a spot next week in the PGA Championship at Bellerive Country Club in St. Louis.
McIlroy won at Bay Hill in March and has three runner-up finishes, and he had said Saturday afternoon he was exhausted of finishing second.
Thomas captured his first World Golf Championship and heads to his title defense at the PGA Championship with plenty of momentum. He can't say that anymore.