Mauney used three birdies at the end of his round to vault ahead of Gilder and Larry Nelson, who also posted a 63 on Saturday. At 16, Mauney hit an 8-iron onto the green and then drained a 22-footer for birdie.
The 17th proved to be an important hole on Saturday as Mauney ran home a 12-foot breaking birdie putt and Gilder, who had the lead at that time, missed a 10-foot par save. The two-shot swing knotted the players at the top of the leaderboard.
Mauney birdied the last after he reached the green in two at the 510-yard hole. He two-putted from 50 feet to gain his one-shot edge.
'The last three holes were awesome,' said Mauney, who earned his playing privileges on the Senior Tour at the 2000 Qualifying Tournament. 'The putt at 17 was the best putt I hit all day. The two- shot swing was key. I knew the game was on then.'
Mauney opened with birdies at two and three and then ran off six pars, including a six-foot save at nine after he drove into the trees.
He started his back nine with with birdies at 10 and 11, which were a pair of five-footers thanks to great wedge shots. Mauney drilled a 15-footer at the 13th before his birdie run at the end.
Gilder had the lead all to himself for a good portion of Saturday's third round but struggled coming in. He bogeyed the 16th when he missed the green right and could not save par from five feet.
'I was going real well until that poor shot at 16,' said Gilder, who won this year's Verizon Classic. 'I hit a poor putt at 17 and a poor chip at 18. That's okay. Other than the last three holes, I played really well.'
Nelson flew up the board on Saturday thanks to an eagle at the par-four 12th when he holed his second shot from 109 yards. He had an eagle opportunity from 12 feet at No. 15 but had to settle for birdie. Nelson closed with a six-foot birdie at 18.
Nelson's 63 on Saturday matched his lowest career round. He is alone in third at 9-under.
Tom Kite and John Bland joined overnight leaders Dave Stockton and Jose Maria Canizares in fourth at 7-under 135.
Bruce Fleisher and Dana Quigley, also co-leaders after round-one, share eighth with Hale Irwin, six shots behind Mauney at 6-under.
See Full-Field scores from the Toshiba Senior Classic here.