On a day in which temperatures soared well past 100 degrees at the Congressional Country Club, Mahan shot a 5-under 65 for a 36-hole total of 135.
Singh walked around the course with a wet towel over his head and players took other precautions to survive the hot day.
Tiger Woods, who like Mahan and Jason Dufner has won twice on the tour this season, holed a 48-foot eagle putt at the par-5 16th to shoot a 68 and jump into a share of 11th place at 140. First-round leader Bo Van Pelt was at 140 after shooting a 73.
Mahan won the World Match Play Championship and the Houston Open in a span of four starts. He has not had another Top 10 finish, but he wound up 11th last week at the Travelers Championship when he shot a 61 in the final round.
Mahan made seven birdies Friday and did not make more than a 4 on any hole.