Sterne has fired two 64s in a row to get to 13-under 203, a shot in front of Oliver Wilson.
Former champion Retief Goosen briefly shared the lead Saturday, but stumbled to an even-par 72 that left him tied for fifth place at 208.
Both Sterne and Haig shot 64 on Friday to equal the record over the Greg Norman-designed Blue Canyon Country Club course. Sterne's good play came after he opened the tournament with a 3-over 75.
"I checked out of my hotel Friday and took my bags to the course," said Sterne, admitting he thought he would miss the 36-hole cut. "I had a flight home at 8 p.m. that I fully expected to be on."