Mickelson fired an 8-under 64 to share the lead as he seeks his third win in four events and Woods, needing just 22 putts for 18 holes, was one shot back.
Woods was joined at 7-under 65 by Harrison Frazar. Woods would regain the No. 1 spot in the world rankings with a win this week and he ended his round by holing a 12-foot par putt.
"I had not made a bogey all day so it was nice to end the day without making a bogey," Woods said.
Mickelson birdied half the holes on the Doral Blue Monster Course and bogeyed the 10th.
"It's a good start to the tournament," Mickelson said. "It's nice to play well, especially when the field is so strong."