Bobby Wadkins, the overnight leader who is battling back problems, struggled to a 2-over 74 on Saturday. He is tied for third place with Hubert Green (68), Tom Purtzer (69) and Dave Barr (70) at 4-under par.
Morgan, who trailed Wadkins by four at the start of the second round, broke out the gate with a pair of birdies at one and three but two bogeys erased his move up the leaderboard.
The 56-year-old missed the green at the ninth and hit a poor chip 15 feet from the hole. He two-putted there for bogey and dumped his tee ball into the water at 12 for his second mishap of the round.
Morgan got his round going at the par-5 14th. He knocked it on in two and two-putted from 30 feet for his third, but certainly not his last, birdie of the round.
At the 16th, he landed an 8-iron 12 feet from the hole to set up birdie and reach 4-under par. He followed with a five-foot birdie at the par-3 17th and another five-footer for birdie at the par-5 closing hole to collect three birdies in a row and assume the top spot on the leaderboard.
'I was glad to finish with three birdies, especially at 17,' said Morgan, who holds a Doctor of Optometry degree. 'The wind direction was more of a factor. It switched around from yesterday. I wasn't very stable out there.'
If Morgan can hold on and visit the winner's circle Sunday, it will be the 22nd time since joining the Champions Tour in 1996.
'I've accomplished quite a bit on this tour,' said Morgan, whose last win came at the 2002 BellSouth Senior Classic at Opryland. 'I've won seven straight years out here and it would be nice to extend the streak early this year.'
Davis took sole possession of the lead midway through the back nine, thanks in part to Wadkins' mistakes and his own beautiful iron play. At 12, Davis fired a 6-iron 10 feet from the hole and cashed in on the birdie chance. One hole later, Davis once again hit a great 6-iron, leaving him with a 12-footer for birdie and sending him to 5-under par for the tournament.
Davis left his tee shot short of the green at 17 but the ball landed in rough in front of a bunker. He chipped his second 20 feet short of the hole and two-putted for a bogey.
The 51-year-old from Australia rebounded at 18 with a five-foot birdie to polish off a round of 2-under 70.
'You have to be patient out there. It was hard to pick the wind out there,' said Davis. 'It could be an interesting day tomorrow.'
Wadkins flushed his ball into the water at 12 and took double-bogey. Over the next six holes, Wadkins mixed two birdies and two bogeys to finish two shots out of the lead.
Gary Koch, the NBC analyst who is making his Champions Tour debut this week, managed an even-par 72 Saturday. He is tied for seventh at 3-under with Allen Doyle and Christy O'Connor, who aced the 12th hole in the second round.