Long-hitting Dustin Johnson was alone in third at eight under after a 66, one stroke in front of fellow Americans Scott Brown (71) and Billy Horschel (70), and Scotland's Martin Laird (68).
Veteran Choi, an eight-time winner on the PGA Tour who has not triumphed on the circuit since the 2011 Players Championship, birdied three of his last five holes on the easier North Course to move joint top.
"My putting hasn't been too good inside 15-20 feet, but today I made five or six outside 15 feet," Choi, 45, told Golf Channel.
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"I heard the weekend will be very windy and rainy, so I'm hoping my imagination, my driving and putting will be stable."
Power hitter Woodlands, winless on the PGA Tour since the 2013 Reno-Tahoe Open, piled up five birdies on his front nine to reach the turn in a flawless five-under 31.
REBOUND ON FINAL HOLE
Though he stumbled late on with bogeys at the 16th and 17th, he rebounded by getting up-and-down from a greenside bunker to birdie the par-five 18th on the challenging South layout.
"The way I'm driving the ball right now, I'm very comfortable with my golf swing," said Woodlands, who made an equipment change during the off-season.
Australian world number two Day withdrew from the pro-am competition on Wednesday because of a virus he picked up last Friday and was unable to practise ahead of his title defence until his warm-up session for Thursday's opening round.
"That was the frustrating part, knowing that I wasn't able to prepare the way I wanted to," said Day, who followed his first-round 72 with a two-over 74 to miss the cut by three strokes.
"I'm not trying to make any excuses. I'm just looking forward to getting over this virus that has run through our family."
American Fowler, who won the European Tour's Abu Dhabi Championship on Sunday, almost holed a greenside bunker shot on his final hole but had to settle for a closing par and a 71 that left him one shot outside the cutline.
Mickelson bogeyed four of his last six holes for a 76 and a one-over total. On his ninth hole, a wild second shot ended up in a car park but his ball bounced back underneath an iron fence marking out-of-bounds, thereby saving him a penalty stroke.
To play his third shot there, the American left-hander walked to the car park side of the fence to make a swing from where he banged his club on the fence before finishing up with a double-bogey seven.
(Reporting by Tim Wharnsby in Toronto; Editing by Mark Lamport-Stokes)
