Langer fired a 66 and Simpson a 67 in the second round at the Crosswater Golf Club in Bend, Ore.
Langer lost a bid for sole possession of the lead with bogeys on two of the last three holes. Simpson birdied 15 and 17.
"I have hit the ball incredibly well over the last two days," Simpson said. "I don't think I've missed but three greens all week and two of the three were on the fringe. I missed 11 today and that led to bogey."