"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.
Schwartzel and Koepka settled for 63s, matching the tournament record with the first same-day 63s in the event's 100-year history, while Kisner shot 64. That was barely enough for a one-shot lead over Kevin Kisner, one of three players who came to the final hole with a shot at becoming the first to post a 62 in the PGA.
He watched playing partners McIlroy and Woods immediately birdie the par-five eighth on resumption, with the Northern Irishman picking up two further birdies to move to three under, seven shots off the lead.
Koepka is in third place at 8-under-par for the tournament.
And with more rain that pounded Bellerive and wiped out golf for the rest of the afternoon, Woodland wasn't even sure he would be leading after the second round was completed.More news: Elon Musk says taking Tesla private is 'best path forward'
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The third round was due to begin about 30 minutes after the end of the second round on Saturday, with players going out in groups of three - instead of the traditional two - off the first and 10th tees.
Woodland, the former Kansas golfer, was off to a scorching start and was at 10-under through the first two rounds at the Bellerive Country Club in St. Louis. So guys, I think we'll see some putts go in. "This golf course is stacked right now and everyone is bunched".
"I feel safe because I feel safe where my game is, " he said. "I'm not too anxious with what anyone else is doing out there". The golf course is gettable and I'm holing a few putts.
"I'm very happy with where I'm at", he said.
"I just love how calm he is out there, " Kisner said. "We're going to have a pretty good battle if I can keep up with him". Kisner is not. He relies more on a clean hit with his irons and a great short game. "Sometimes you are in your own mind and don't know where you are at".
Said Woodland: "I have a lot of friends out here, a lot of college teammates, a lot of people from college". I have more people coming in this weekend.