McGirt rode a hot putter to eight birdies, including five in the first six holes, ending at 12-under-par 201 at Riviera Country.
Before Saturday, the 34-year-old American had never held a 54-hole lead on the PGA Tour. His best finish came at the 2012 Canadian Open, where he was runner-up.
Sharing second place at 10-under were George McNeill (66) and Charlie Beljan (68).
Jason Allred (67) and Brian Harman (68) knotted for fourth one shot further back.
Overnight leader Sang-Moon Bae stumbled to a 1-over 72, dropping into a sixth-place tie at 8-under with Bubba Watson (64), Cameron Tringale (67), Jimmy Walker (67), Jordan Spieth (67,) Charl Schwartzel (68) and Dustin Johnson (69).