One shot off the pace overnight, the 27-year-old American fired a nine-under-par 63 on the Nicklaus Private course at PGA West, one of three venues hosting the tournament renowned for its low scoring in the California desert.
Bidding for a third victory on the US PGA Tour, Stallings eagled the par-five 13th and eighth after starting out at the 10th to take command with a 22-under total of 194 in the pro-am celebrity event.
"I feel good," Stallings said after scrambling well in a round that also included five birdies. "I played well. I stayed aggressive. I've been smart when I got out of position.
"I guess you can say it's conservatively aggressive. Like number eight today, I hit a really good drive and had eight iron," he said of his second eagle.
"But just because I had eight iron to a par-five, I fired it in the middle of the green, had a 20-footer and was happy to make it."
Former Open champion Stewart Cink, who has struggled for consistency over the past four years, carded a 66 on the Palmer layout to share second place with fellow American Roberto Castro (69), co-leader overnight with rookie James Hahn.
Also at 17 under with Cink and Castro after another ideal day for scoring with hardly a breath of wind in the sun-drenched Coachella Valley were Americans Charles Howell III (67), John Rollins (64) and Charley Hoffman (67).
Little-known American Brian Stuard was a further stroke back after shooting the best round of the week, a 62 on the Palmer course, putting him among a group of eight including compatriot Kevin Streelman (66) and South Korean Bae Sang-moon (64).
Twice former champion Phil Mickelson flirted with the cut for much of the day but eventually made sure he would qualify for Sunday's final round after completing a six-birdie 66 to finish at 11-under 205.
A stroke outside the cutline with three holes to play, the American left-hander finished strongly with birdies at 16 and 17 before parring the last despite dumping his second shot into water.
Rollins was Stallings' playing partner for a third consecutive day, a pairing which has so far proved beneficial for the tournament leader.
"Playing with John was a huge help," said Stallings, who is the only player in the field without a bogey in the first three rounds. "He's a good guy and he was an easy guy to club off of. He played well just like I did.
"We have made a lot of birdies the last couple of days, and so we kind of fed off each other. That's definitely what you need to try to do in this format," said the American, who was hampered by a rib injury for much of his 2012 campaign.
Asked what his strategy would be for Sunday's final round on the Palmer Private layout, Stallings replied: "Go do the same thing I've done for the last three days. I've been aggressive.
"Obviously, a lot can happen coming down the back nine, especially with all the birdie holes, but it is what it is. I'll go out there, try to be aggressive early and go from there."
Cink, who has not won on the US PGA Tour since his play-off victory in the 2009 British Open at Turnberry, was pessimistic about his chances of coming from five strokes behind going into the final round.
"You're five shots back on a course where the leader is probably not going to back up very much at all," he said.
"A five-shot deficit could come back in the first nine holes because there's some more bogey holes, but here you wouldn't expect that quite as much."
The cut fell at 10-under 206 with US Open champion Webb Simpson, 2008 Masters winner Trevor Immelman and defending champion Mark Wilson among those failing to advance.
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