Adam Scott posted a fine 65, his second in a row, to get to ten under par and will play in the final group on Sunday alongside Koepka.
Gary Woodland shot 66 before rain halted play in the afternoon, and finished at 10-under 130.
Kisner made bogey on No. 9 and finished the day with a 64, one stroke behind Woodland and one ahead of Brooks Koepka, victor of the past two U.S. Opens.
Tiger Woods is now three-under but the American multiple major victor was only through seven holes of his second round when play was stopped. "I was giving him crap because he let us down on the back nine with only three birdies".
"After the Open I wanted to do something different, just change the way I thought I on the golf course and he's been brilliant so far". So guys, I think we'll see some putts go in.
The 14-time major victor was three under for his round to that point and carried on where he left off on Saturday morning, pitching to five feet and holing the putt to improve to four under par.
Schwartzel, the 2011 Masters victor, didn't threaten the lead with his run at 62 but sank a seven-foot birdie putt at the par-3 16th to reach 7-under.
"It seemed like that was the only way I was going to make birdie, hit it to tap-in distance or chip in", McIlroy said.
World number one Dustin Johnson is just three shots off the pace after carding five birdies in six holes on his way to a 66, with Open champion Francesco Molinari another two shots back after a 67.
That Woods stalled on the back nine wasn't completely surprising, at least not this year.
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But the nail in the coffin was not even being on the bench during Chelsea's recent Community Shield loss to Manchester City . CHELSEA star Willian has spoken about Barcelona's attempts to sign him after insisting he is happy to remain at the club.
Li opened with a 1-over 71 and was 3 over for the championship.
"I played really well", Koepka said.
Having been part of Friday's afternoon wave forced to return on Saturday morning, his chances of extending his stay were ended by a double bogey at the par three 16th.
Koepka birdied the eighth but missed a 19-foot birdie putt at nine for a 62, settling for a 63, matching the lowest round in tournament history.
He picked up one last birdie when he reached the green in two on the 597-yard 17th hole and two-putted, sending him to a 66. "Sometimes you are in your own mind and don't know where you are at".
"I've got my work cut out for me tomorrow", said Woods, who is at 8-under 202. He stood at 7 under with eight holes left to play. Of course, we've all been there, save the part about playing in a major and actually being good enough to warrant being ticked off at missing a fairway.
Spieth still has hope in his second try at a career Grand Slam.
"Everyone's going to have to shoot low rounds", said Woods.
Three weeks ago, Woods trailed the leaders by four strokes heading into the final round at Carnoustie, and found himself atop the leaderboard with eight holes to go before finishing in a tie for sixth.