Nick Watney and Dustin Johnson, who had both failed to break 80 when leading Majors with a day to go last season, were level on 15 under par with four holes to go in the second of this year's WGC events.
The pair were two in front of Dane Anders Hansen and Italian Francesco Molinari, who had taken over at the head of Europe's challenge with World Number Three Luke Donald, joint second overnight, falling four back, Rory McIlroy six behind and Padraig Harrington seven adrift after a round which included two trips to the water on the third for a triple-bogey seven.
And that after he had opened with a 15 foot eagle putt to be in a tie for second spot.
Woods was alongside the Dubliner on eight under after a 66 that brought him from 30th to tenth.
It came too late to make him a threat to the leaders, but was huge encouragement to the former World Number One with The Masters Tournament only three weeks ago.
"It's progressing. I'm still building, still putting the pieces together, which is nice," he said.
"I hit a lot of good shots and when I did miss it I knew how to fix it."
He has now gone 19 events and 16 months without a victory, while Mickelson is up to 22 events stretching back to last April's Masters Tournament after a closing 76 for a four over aggregate.
Lee Westwood gave his confidence a boost like Woods with a 68 for six under and with Donald unlikely to win he seemed sure to remain second on the Official World Golf Ranking to Martin Kaymer, who had fallen away over the weekend with two rounds of 74.
Donald needed to win to move ahead of Westwood, but was in the water like Harrington on the third and after coming back with two birdies further bogeys at the 11th and 13th appeared to have taken him out of the equation.
McIlroy was only two behind after two-putting the first for birdie, but he could hardly stay out of sand as his bid for a second victory on American soil faded.
Scot Martin Laird slipped out of the picture too from only four back at the start of the day.