Woodland bounced back from an opening bogey to shoot 6-under 64, moving him ahead of early leader Rickie Fowler at Bellerive.
Woodland was still scuffling along at one-over until making birdie at the par-5 eighth. He added another to close out the front nine, then got hot over the final eight holes, making five birdies and steadily climbing the leaderboard on steaming afternoon.
Woodland got off to a good start last year, too. The Kansan shot 68 at Quail Hollow and was still within sight of the leaders entering the final round, when a 74 left him in a tie for 22nd.
Fowler sits a shot back at five-under with a 65, tied for his best score in a major. South Africa's Brandon Stone is at four-under while 13 players are at three-under including Dustin Johnson, Ian Poulter, Jason Day and Justin Rose.
Tiger Woods rallied from a bogey-double bogey start to shoot an even-par 70.
Woods missed his first two fairways and dumped an approach shot in the water. But scrambled for enough pars to keep his round going, then made a pair of birdies on a bogey-free second nine.
Playing partner Justin Thomas was one-under and Rory McIlroy also was even.