Bidding for his third victory of the year in five starts, Woods picked up shots at three of the first four holes before covering the back nine in five-under 31.
That left him one ahead of fellow Americans Mickelson, 2002 U.S. PGA champion Rich Beem, Ryan Palmer and Mark Wilson, plus PGA Tour rookie Camilo Villegas of Colombia.
"I drove the ball really well today," Woods told reporters after a day of near-perfect scoring conditions.
"Some of the things that I've been working on are starting to come together. I played like this at La Costa, only difference is today I made putts."
Woods romped to a record 9&8 victory over Canadian Stephen Ames in his first match of last week's WGC-Accenture Match Play Championship at La Costa before being ousted in the third round.
"Any time you get receptive greens and smooth greens, and this morning absolutely no wind, the guys are going to go low," the U.S. Masters and British Open champion added.
"This afternoon it blew a little bit, but it wasn't that bad. Tomorrow more than likely we'll probably get the same conditions the guys got this morning and no wind.
"Hopefully I can go out and post another good number, because you have to. If you shoot even par, you're going to get run over here."
Left-hander Mickelson was delighted to find some form with his putter after struggling on the greens in his first five PGA Tour starts of the year.
"I putted well today," the world number five said. "You can't shoot six or seven under par without putting well.
"I ended up rolling some good putts in. It was a fun day, a fun start. A lot of low scores, but I'm glad to be one of them."
Among the other big names, Sony Open winner David Toms was one of five players who opened with 66s while world number two Vijay Singh returned a 67.
Davis Love III, who lost to Australia's Geoff Ogilvy in the final of the WGC-Accenture Match Play Championship at La Costa on Sunday, and Ireland's Padraig Harrington were among a group on 68.
Spaniard Sergio Garcia, the world number six, birdied his final hole for a 69 while twice U.S. Open champion Retief Goosen, the world number three, carded a 70.
However, fourth-ranked Ernie Els finished eight strokes off the pace, offsetting four birdies with four bogeys for a level-par 72 in his first appearance at Doral since his 2002 triumph.
Nine of the world's top 10 are playing this week at the Blue Course, where the tournament is being held for the final time as a regular tour stop.
Next year, it will be replaced by the elite WGC-CA Championship, one of four World Golf Championships (WGC) events held during the season for the world's top 64 players.