Bob Gilder, who won the Constellation Energy Classic two weeks ago, matched Eaks' 66 to move into second place at 10-under-par 134.
Allianz Championship winner Tom Jenkins posted the lowest round of the day as he carded 7-under 65. He is alone in third at minus-9, while Rodger Davis is at 8-under-par 136 after a 66.
Eaks opened his round with five straight pars before catching fire. He dropped in a 10-foot birdie putt on the par-4 sixth. Eaks, who owns three wins on the Nationwide Tour, made it two in a row as he birdied the seventh.
The 53-year-old moved to 8 under as his short birdie try on the ninth found the bottom of the cup. Eaks stumbled to his only bogey on the 10th, but bounced right back with a birdie on the par-3 11th.
Eaks, whose best Champions Tour finish was a tie for sixth earlier this year at the Commerce Bank Championship, moved to minus-9 with a birdie on the par-4 13th. He closed with an 11-foot birdie putt on 15 and a 6-footer for birdie at the 17th to lead by one.
'That was a great pairing for me,' said Eaks of playing with Gilder and Bruce Summerhays. 'They just dragged me along. I had some chances early, but just wasn't making any putts. All in all, I am happy with my game and excited for tomorrow.'
Gilder drained a birdie on the second, but slipped to a three-putt bogey at the next. The 54-year-old came back with a birdie on the par-4 fourth. He moved to minus-6 with a birdie from 10 feet out on the sixth.
The eight-time winner on the Champions Tour holed a 7-iron from 164 yards out for eagle on the par-4 10th.
Gilder got to 9 under with a birdie on the par-4 13th. He bogeyed the next after finding water, but converted back-to-back birdies from the 16th to get to 10 under. He closed with a pair of pars to take second place.
'I'm making birdies which is good. I feel aggressive and my irons feel good in my hands,' Gilder said. 'I'm kind of a streaky player and I like the streak I am on now.'
Craig Stadler, the defending champion, carded a 6-under 66 to move into a share of fifth place at 7-under-par 137. He was joined there by first- round leader Summerhays (71), Gary McCord (67), Hale Irwin (68) and Danny Edwards (68).
Former U.S. Open champion Scott Simpson, who is making his Champions Tour debut this week, posted an even-par 72. He dropped into a share of 14th at minus-4.