Woodland is a three-time victor on the PGA Tour but has never won a major championship.
After birdieing five of his first eight holes and playing the front side in 31 strokes, Woods stalled on the back nine, failing to convert any birdie opportunities and squandering a handsome chance at the par-5 17th, where he three-putted for par.
Watson, who finished second at the PGA in 2010, was even-par to start the day, and he was still just 1 over after a birdie at the par-5 17th.
But he then sandwiched two five-foot par putt misses for bogeys at the 10th and 12th holes around a birdie from half that distance at the 11th.
Round One leader Gary Woodland shot a four under par 66 to get to 10 under for the tournament and hold on to the lead.
Kisner birdied the seventh hole, his 16th of the day, to reach 7-under but found a bunker to par the par-5 eighth and chipped 25 feet beyond the cup and two-putted to bogey nine for a 64.
Thomas, trying to join Woods as the only back-to-back winners of the PGA Championship since it changed to stroke play in 1958, ran off four birdies on the back nine for a 65 that left him in the group at 6-under 134.
"The golf course is good", said Woodland, a three-time PGA Tour victor who has never finished among the top 10 in a major championship.
"Butch [Harmon] and I focused so hard this year on driving the golf ball because, when I drive it in play, I'm playing a game a lot of guys aren't playing out here, and that's a huge advantage".
The 25-year-old is without a win since victory in the Open at Royal Birkdale last year and 12 months on there would be no repeat at Carnoustie, where he went into the final round with a share of the lead but stumbled to a closing, birdie-free 76.
Woods has played the front nine in 10 under this week but is two over for the back nine. "I didn't even think of (the 62)". He stood at 7 under with eight holes left to play.
"That was enough to make me play a little more freely".
McIlroy's birdie on the par-five eighth was his first since his fourth hole on Thursday and he also chipped in on the 14th after flying the green with his approach.
Tiger Woods, who won his 14th major in 2008, shot 66 to end on eight under. "This is the first real Tiger effect, I guess you could say".
No player in USA history has featured in more Ryder Cups than Mickelson, who has played in a total of 45 matches.
Jordan Spieth's career Grand Slam chances vanished with an ugly - and unusual - triple bogey on Saturday at the PGA Championship.