Hale Irwin, the all-time wins leader on the Champions Tour with 38, and Dave Barr of Canada also posted rounds of 68 to share second place at 10-under-par 134. Craig Stadler and Gary Koch were one shot further back at 9-under-par 135.
After matching the course record at Savannah Harbor Golf Resort and Spa with a 65 on Friday, Morgan, who is leading the money race on the Champions Tour, had plenty of work ahead of him to hold the outright position under optimal scoring conditions.
While several players made early moves on Saturday, Morgan tallied a lone birdie on the front nine to make the turn at 8 under.
Morgan got things rolling on the inward half with back-to-back birdies from the 10th before dropping a shot with a bogey at the 12th. He recovered with a birdie at the 14th and played his approach inside 12 feet for a birdie at the par-4 16th to reach 11 under.
The 57-year-old parred his two remaining holes to carry a slight edge into Sunday's final round when Morgan will attempt to become the first two-time winner on the Champions Tour this season.
'I didn't play as well as I'd like on the front side,' said Morgan, who captured the SBC Classic earlier this season. 'I felt like I didn't get the ball as close to the hole as I'd like. I'd like a few more birdie chances in the final round.'
Irwin had a rocky start to his round with a bogey at the first. He birdied the second and the fourth but found further trouble with a double bogey at the par-4 sixth.
The 58-year-old countered with a birdie at the following hole and picked up the first of three consecutive birdies at the par-4 ninth to climb to minus-9.
At the par-4 18th, Irwin knocked his second shot to seven feet and converted the birdie putt to finish one shot off the lead.
Bruce Fleisher, who won this year's Royal Caribbean Golf Classic, shot a 69 to join Don Pooley in a tie for sixth at 7-under-par 137.
Larry Nelson, Tom Purtzer, John Jacobs and Leonard Thompson shared eighth place at 6-under-par 138.
Defending champion Bruce Lietzke carded an even-par 72 to finish nine shots off the pace in a group at 2-under-par 142.