Finau had five birdies in his first 10 holes, but then he double bogeyed the 11th when his ball landed on a sprinkler head beside the green and kicked into a hazard.
Rose was trying to join Woods as the only players to successfully defend a WGC title Woods has done it eight times and birdied the 13th and 14th holes to pull within one shot of the lead.
A Ryder Cup hero for Europe in Paris, Fleetwood finished with a birdie for a 72 and a share of fifth with American Andrew Putnam, who shot a 67 to move to eight-under for the tournament.
The South Korean-born New Zealander had five birdies on her front nine then stalled somewhat on the back nine until an approach to one foot on the par-4 17th, a shot she called "one of the best of my career", resulted in a birdie.
"That was about as bad a break as I've ever had, to kick all the way over the green into the hazard", Finau said. At the Open Championship at Carnoustie, Scotland, Schauffele and Finau played together for two rounds and both finished in the top 10, with Schauffele edging Finau by two shots, finishing in a tie for second while Finau tied for ninth.More news: Mattis looks to calm European allies nervous about INF treaty
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Reed had been bogey-free in his opening 64.
Rose has a chance to return to No. 1 with a victory, and it doesn't look as though Brooks Koepka can put up much of a fight.
"It means a lot, last season I really wanted to justify my rookie year by winning but I wasn't able to do it", the Californian said. The U.S.is trying to become the first country to have four players win all four World Golf Championships in one year after Phil Mickelson won the Mexico Championship, Bubba Watson won the Match Play and Justin Thomas won the Bridgestone Invitational at Firestone.
The feature group was anything but that - Johnson, Rory McIlroy and Francesco Molinari combined to shoot 6-over par.
This was Finau's first tournament of the season and like past year, he went home with a second-place finish.
If Xiong, who turns 20 on November 9, triumphs Sunday, he would become only the second teenager to win on the PGA Tour since 1931.