Bae produced a faultless round en route to his five-under par 66 as the second round was suspended due to darkness at the Riviera Country Club in California.
But only three players inside the projected cut were unable to complete their rounds.
Bae started the day in second position but five birdies, two of those in succession at the 16th and 17th, propelled him to the top of the leaderboard at nine under.
Australian Aaron Baddeley (65) and American Robert Garrigus (67) are one shot adrift heading into the third round.
Baddeley, who has not won a PGA Tour title since his triumph at Riviera in 2011, climbed up the leaderboard late in the day after birdying his final four holes, while Garrigus produced an eagle at the 17th.
American Charlie Beljan is in sole possession of fourth spot, two shots off the pace.
Compatriot Dustin Johnson surrendered his overnight lead following a round of 70, which included three bogeys.
Johnson is joined by fellow Americans Brian Harman (69), William McGirt (67) and Jim Furyk at six under.
American quartet Blake Adams (70), George McNeill (68), Jason Allred (64) and Scott Brown (67), and South African Charl Schwartzel (68) are all a shot further back.
In-form American Jimmy Walker, who claimed his third title of the season after emerging triumphant at the Pebble Beach National Pro-Am last week, could only manage a round of 71 as he dropped 12 spots.
Walker is four under alongside the likes of Keegan Bradley (70), Kevin Stadler (69) and Charley Hoffman (71).
Englishman and former world number one Lee Westwood, who parted ways with coach Sean Foley before Thursday's opening round, carded a round of 70 to be six shots adrift of Bae, while South African veteran Ernie Els (70) is well off the pace at one under.
Aaron Baddeley one shot behind Bae at Riviera
