Xander Schauffele shot a 67 to share third with Jon Rahm (68), Chez Reavie (71) and Rose (74) at seven under. Scott, who made an early charge with an eagle and two birdies in a front-nine 31, cooled off on the final nine and settled for a 68 and a tie for seventh, at six under, with the 2010 British Open champion, Louis Oosthuizen (72).

Rose, the 2013 champion, pulled even with Woodland with an opening birdie, but he bogeyed the second. He could not keep pace with Woodland, who played the first eight holes in two under to keep a charging Koepka at bay. Koepka began the day four strokes behind Woodland, who was winless the previous seven times he held the 54-hole lead, and, aided by eight one-putt greens, played the first 11 holes in four under par to pull to a single stroke behind Woodland.

“All right, man, we’ve got a ballgame now,” Koepka said he was thinking. But despite shooting in the 60s all four rounds, Koepka could not keep up with Woodland, whose 69 equaled his highest score of the week.

“Props to him for the way he hung in there,” Koepka said.

Woodland, who played basketball at Division II Washburn before transferring to Kansas for golf, said he learned how to control his adrenaline, contain his emotions and play within himself while paired with Woods in the final round of last year’s P.G.A. Championship. Woods ended up finishing second to Koepka, four strokes ahead of Woodland, whose tie for sixth was his best showing in a major until Sunday.