World number two Mickelson finished the day at 14-under for the tournament, while Woods and Nick Watney, who shared the lead overnight, both shot 70s to ensure an all-American leading group on Sunday.
Despite being the best two players in the world in recent years, Woods and Mickelson have not often been put together in the leading group final round with a title up for grabs.
Mickelson, who won here in 2007, picked up three shots in his first five holes to join Woods and Watney at the top of the leaderboard before dropping off with a bogey five when he found the trees at the ninth.
Woods, playing a hole behind his rival, had reaped the benefit of superb approach shots at the second and fifth holes to convert short putts for birdies that put him on 12-under.
The 14-times major champion then drained a nine-foot putt at the eighth to take the lead on his own for the first time in the tournament but was pegged back when his drive found a bunker on the ninth fairway and he missed a six-footer for par.
Another birdie straight after the turn was cancelled out by a bogey at the 11th and he could only manage pars down the remainder of the back nine, recovering well after finding the rough with his drive and bunker with his approach at the last.
Up ahead, Mickelson also played par golf before his round reignited with birdies at the 14th and 15th and he completed his 67 with a huge grin on his face after another at the signature 18th.
"It was a good round and I was pleased to shoot a 67 ... I didn't make too many big mistakes," said Mickelson, who won the WGC-CA Championship earlier this year.
Another American, Ryan Moore, chipped in for eagle at the second but bogeys either side of the turn hurt his cause. He rallied with birdies at his last two holes for a 70 to remain alone in fourth, three shots off the pace.
Briton Lee Westwood, who leads the European Tour's "Race to Dubai" standings, bagged eight birdies for a superb 65 to put at least one non-American on the leaderboard in fifth place at 10 under.










