The Bridgestone Invitational, played at Firestone Country Club in Akron, Ohio, is one of four invitation-only World Golf Championships events on the tour.
Woods, an eight-time victor at Firestone, took the advantage at the hard par-4 18th hole (his ninth) when he drained a 50-foot monster birdie putt to climb to three under.
Thomas shot 15-under for the tournament, beating second-place finisher Kyle Stanley by four shots.
Rory McIlroy is joined by Ian Poulter, who has sat atop the leaderboard much of this tournament, three shots back of Thomas at T2. He chipped 50 feet by the hole and three-putted for a double bogey, the start of what turned out to be a sloppy day and a 74 that dropped him seven shots behind.
Fleetwood, a four-time victor on the European Tour who has flashed impressive form in all three majors this year but remains in search of a first title in the United States. "I was putting it in position where I should have been giving myself birdie chances and I was having to hole five and six-footers for par, so I think my patience was rewarded". That made his steady play all the more meaningful for him.
"We sat down and just said, what are we doing wrong?" The last player to win two of these in a row is (you guessed it) Woods in 2006 and 2007.
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"I didn't warm up very well".
The World Golf Championships in Akron has a yearly economic impact of more than $21 million according to Firestone's website.
"I'm going to have to", Woods said. The 22-year-old was one of three rookies and 24 first-timers, including seven making their WGC debuts.
Day, the 2015 PGA Championship victor, is similarly confident of sharpening up in time for a bid at an anticipated second major title.
"It is the first time I have cried after winning a tournament".
Their relationship goes back more than a decade, back to junior golf days and at rival colleges, where each could hold their own share of bragging rights.
Bridgestone shifted its title sponsorship to the PGA Tour Champions, which will bring its Senior Players Championship to Firestone next year. "With a three-shot lead, I obviously knew that I needed to play well, but you kind of have a little bit of wiggle room and you feel like you maybe play a little too conservative, but I was able to kind of dwell on past learning experiences and you always try to get it higher".