Mahaffey's round broke the course record at Silverado Country Club by one. Dale Douglass originally shot a 63 in 1991 and was later matched by Bob Charles a year later and Isao Aoki in 1994.
Ted Goin is alone in fourth at 10-under followed by Bob Gilder, whose second-round 64 gave him a 9-under 135 for the tournament.
Mahaffey wasted no time moving up the leaderboard on Saturday as he birdied his first seven holes, including four putts from inside four feet. He kept his front nine flawless when he ran home a six-foot par save at the ninth for a 7-under 28.
'I really wanted to shoot in the 50s,' said Mahaffey, whose seven birdies in a row fell one short of the all-time Senior Tour record. 'I wanted to keep being aggressive and see what I could do.'
Mahaffey kept his hot streak going with a five-foot birdie at the par-5 11th and added a four-footer at 14. His only mistake of the round came at the 330-yard 16th when his approach spun off the green. He chipped on but two-putted for bogey.
He closed his round in style with a 12-foot birdie at the par-3 17th and a two-putt birdie from 30 feet at the closing hole at the South Course at Silverado Country Club.
'It's nice to see the golf ball going where you think it's going,' said Mahaffey, the 1978 PGA Champion who has won only once on the elder circuit. 'I really didn't make a mistake. Everything went right where I was looking. It was fun.'
Rachels made four birdies on the front nine but turned it up on the back. He ran in a 20-foot birdie putt at No. 11 and then tallied three birdies in a row, starting on the 13th.
The 51-year-old played his second shot at the par-5 18th into a greenside bunker where he blasted out to four feet to set up birdie and join Mahaffey at the top of the leaderboard.
'It was a great day for me,' said Rachels, the winner of this year's BellSouth Senior Classic at Opryland. 'I really putted well. It's hard to shoot 63 and get beat.'
Doyle, who led by one after Friday's first round, three-putted from 20 feet at the third and took bogey and coupled with the surge by Mahaffey and Rachels, found himself out of the lead.
He rebounded with three straight birdies, starting at the fourth to post a 33 on the front side.
Doyle, a two-time winner on tour this year including the final major at the Senior Players Championship, holed an eight-foot birdie at 11 and followed with a 15-foot birdie two holes later. He birdied two of his final three to grab a piece of the lead.
'I saw the low scores early and you had an idea you had to make something happen,' said Doyle. 'I like my chances and I've given myself a shot.'