Larry Nelson carded his second straight round of 4-under 68 to take second place at minus-8. Mike McCullough, one of five overnight leaders along with Morgan, managed a 2-under 70 and stands alone in third place at 7-under-par 137.
Morgan was hot throughout his round. He picked up his first birdie at the par-4 second. He then converted back-to-back birdies from the fourth at Valencia Country Club to get to minus-8.
The reigning Kroger Classic champion continued his climb up the leaderboard with a birdie at the ninth from 15 feet out. Morgan then dropped a sand-wedge within three feet to set up birdie at the 11th to climb to 10-under.
Morgan kept rolling with a birdie at the 13th. He moved to 12-under when he birdied the par-5 15th. He picked up his first bogey since the fifth hole of the first round when he dropped a shot at the 17th, but his lead was safe.
'I felt like I gave one away early on the front not making birdie at the first,' said Morgan. 'I didn't play the last two holes very well either. I'll need to play a good round tomorrow to have an opportunity.'
Morgan knows that two of the last three SBC Classic winners have come from behind to win the event.
Nelson began his day one shot behind the five overnight leaders. He kept pace early on as he rolled off three straight birdies to open his round to quickly move to minus-7.
The 56-year-old Nelson caught fire again around the turn. He rolled in a birdie try at the eighth and made it two straight when he birdied the par-5 ninth.
Nelson made it three in a row when he birdied the 10th to climb to 10 under. He later stumbled to back-to-back bogeys from the 16th to fall back to minus-8.
'I've played well. Maybe the key is not to get off to a good start,' Nelson joked afterwards. 'Gil is a good player. He does everything well, but the lead is not insurmountable.'
Don Pooley and Peter Jacobsen, two of the other overnight leaders each carded rounds of 1-under 71. They stand at 6-under-par 138 along with Mark James, Sam Torrance and Des Smyth.
Craig Stadler, the final of the five overnight leaders, shot an even-par 72 to stay at minus-5. He is joined there by defending champion Tom Purtzer, Allen Doyle and Hale Irwin.