
Singh, of India, and Karlsson, of Sweden, shot 2-under-par 68s at the Oakland Hills Country Club, where players waited out a 90-minute weather delay before play was suspended for the day.
Argentina's Andres Romero, who played 16 holes, also was at 2-under.
Eighteen players on the course when play was suspended will complete their rounds Friday.
Sean O'Hair, Sergio Garcia, Ken Duke and Billy Mayfair were all at 1-under 69.
Singh surrounded three bogeys with a double-eagle and three birdies. Karlsson birdied three in a row from the second, but an opening double-bogey and bogeys at 14 and 15 prevented him from taking an outright lead.
Karlsson had top-10 finishes in the three previous majors this season.
"This is a new event (for me)," he said. "This has nothing to do with the other three."
Phil Mickelson, the 2005 PGA Champion, overcame bogeys at his first two holes to shoot an even-par 70.
"I'm just happy to have shot even-par today," Mickelson said.