Baddeley, a 21-year-old PGA Tour rookie in his first event as a tour member, had three birdies and an eagle before parring every hole on the inward half en route to a 5-under-par 65 in breezy conditions at Waialae Country Club.
"I hit a lot of good shots on the front nine," said Baddeley, who already has won two Australian Open titles and who finished 54 holes at 15-under 195. He led by five strokes at the turn, but Els finished strongly with three birdies in the final five holes to shoot a 66 and cut the gap to two.
"It's going to be exciting, my first time leading a PGA Tour event and playing with the second-best player in the world," Baddeley said.
Baddeley had about 18 balls stolen from his locker overnight but still had about a dozen left for his round, which is about the number he generally uses in the course of 18 holes.
The highlight of his day was an eagle at the par-five ninth, where he sank a 40-foot bomb from the back of the green.
"I'll be coming out aggressively tomorrow, going at the pins," he said. "I'd much rather be two ahead than two behind."
Els, winner of last week's season-opening Mercedes Championships, has a chance to make a perfect start to the season.
He was not at his sparkling best Saturday, especially on the front nine, where he had trouble adjusting to the pace of the greens. But by the end of the day, he was the only player to make a move on Baddeley.
"I didn't play all that great on the front nine but I grinded it out," said Els, who is bidding to become the first player to win the first two events of a season since Steve Jones in 1989. "I'm pleased to be only two back after being five back at one stage."
South African Retief Goosen, who shared the halfway lead with Baddeley, triple-bogeyed the first hole after pushing his drive into an unplayable lie. He shot 72 to fall seven shots off the pace.