Bruce Lietzke and Bruce Fleisher carded matching rounds of 7-under-par 65 and share fourth place at 11-under-par 133.
Stewart Ginn and first-round co-leader Steven Veriato are tied for sixth at minus-10.
Hale Irwin, the reigning Champions Tour Player of the Year, held a piece of the first-round lead but struggled on Saturday. He only managed a 1-under 71 and is part of a group tied for 14th at 7-under par.
Jack Nicklaus and Lee Trevino, both sponsor's exemptions, were only two off the lead after Friday's opening round. Trevino carded a 1-under 71 Saturday to share 21st at 5-under and is one better than Nicklaus, who is alone in 25th at minus-4.
The three leaders equaled Gil Morgan's 36-hole record of 13-under-par 131. Nelson also posted a 131 in 2001 on his way to victory but Zoeller was the player who made the biggest move up the leaderboard on Saturday.
Zoeller was 6-under on his round through 10 holes thanks to four birdies and an eagle at No. 10. He dropped a shot at 11 and carded two pars before an awesome conclusion to his round.
Zoeller drained a pair of 10-foot birdie putts at the par-5 14th and at 15. He holed a 12-foot birdie putt at No. 16 to reach 12-under par and grab a temporary two-shot advantage. He ran home a seven-footer for birdie at the 17th to make it four in a row and, with a par at the last, reach the clubhouse at 13-under par.
'Anyone who plays this stupid game wants to see if they can control it under the heat,' said Zoeller, who tied Tom Kite's course record from last year. 'I worked very hard in the offseason. I played a lot of golf and it was well worth it because it's paying off.'
Nelson was flawless on Saturday with three birdies in his front nine but, like Zoeller, his back nine vaulted him up the leaderboard. He sank a breaking 20- footer for eagle at the 10th to get the run started.
Nelson, who went winless in 2002, tallied three birdies in a row, starting at the 13th. At 14, he narrowly missed an eagle putt but tapped in the birdie. On 15, Nelson holed a eight-foot birdie putt to tie Zoeller in the lead but Nelson missed some birdie chances on his way in that could have given him the outright lead.
The 55-year-old had a 12-footer at 16 but missed that then failed to convert on a nine-footer at the last. Nelson left the course with an 8-under-par 64.
Quigley, who also shared the lead after the first 18, reached 10-under par after a birdie at the 13th but his best was yet to come as sharp iron play down the stretch earned him his share of first.
Quigley knocked his approach close to the hole at 16 for birdie and made it two in a row with a four-footer at the short, par-3 17th. He drained a seven-foot birdie putt at the last to polish off his round of 7-under 65.
'I'm on my game right now and it's kind of fun when you can look up after your shot and see it going towards the flag,' said Quigley, who made his 202nd consecutive start for which he was eligible. 'I'm trying to run the tables and make birdie on every hole.'
Kite (67), Allen Doyle (66), Jay Sigel (69), Tom Jenkins (66), Jim Thorpe (66) and Tom Watson (66) share eighth place at 8-under-par 136.