McGirt birdied five of the opening six holes of the Riviera Country Club on Saturday, with a bogey on the fourth the only blemish for the 34-year-old, while he added three birdies and another bogey on the back nine to move to the top of the leaderboard at 12-under overall.
The American's six-under 65 leaves him two shots ahead of compatriots George McNeill and Charlie Beljan.
As overnight leader San-Moon Bae struggled in California, McGirt, McNeill and Beljan took advantage to give themselves a big chance of clinching the PGA Tour title on Sunday.
McNeill started with an eagle on the par-five first hole and posted a bogey-free back nine with birdies on the 10th and 16th holes to card a five-under 66.
Beljan produced a three-under 68 to join McNeill in a share of second at 10 under, while Jason Allred and Brian Harman are a shot further back, tied for fourth.
Baddeley endured a tough day as he could only manage a one-over 72 to tumble down to a tie for 13th place at seven under, one shot ahead of compatriot John Senden.
Bubba Watson was the big mover of the third round, shooting a seven-under 64 to rise into a share of sixth.
Watson's bogey-free round included seven birdies, including three straight from the eighth hole, as he moved alongside Cameron Tringale, Jimmy Walker, Jordan Spieth, Dustin Johnson, South Africa's Charl Schwartzel and Bae at eight under.
Bae had started the round a shot clear at the top of the leaderboard but four bogeys in his one-over 72, including one on the 18th, left the 27-year-old South Korean four shots behind McGirt.