Former PGA champion David Toms fired a 65 to join Tom Pernice, Jr. and Jeff Brehaut in a tie for second at 10-under-par 134.
Geiberger's lone PGA Tour victory came in 1999 in Hartford, where he also held the 36-hole lead. A win this week would be fitting since his father Al captured the event in 1976.
'I would like to win any of the tournaments he's won,' said Geiberger. 'Any time you win it's special, but it's kind of neat to have won a place your dad has.'
Geiberger parred his first four holes before he picked up his first birdie of the day at the par-4 fifth. He then birdied the par-5 ninth and took advantage of the par-5 holes on the inward half with birdies at the 13th and the 15th.
The 36-year-old capped off his round with a birdie at the par-4 18th to complete his first 36 holes without a bogey.
'Today was a lot tougher than yesterday, that's for sure,' said Geiberger, whose best finish on the PGA Tour this season was a tie for 14th at the Texas Open. 'Pretty proud of not having any bogeys yet. That was one of my goals today was that if I could get around with no bogeys I would be happy with that.'
Toms collected five birdies and a bogey over his first nine holes to make the turn at 7 under. Toms, who already won this year at the St. Jude Classic, added a trio of birdies on the back side to finish within one of the lead.
'It was a tough day to get a lot of opportunities to make birdies and it seemed like when I did, I capitalized on them and when I got in a tough spot I recovered well,' said Toms. 'I wasn't really surprised at the score, it was just a good score considering the conditions.'
Like Geiberger, Brehaut is currently on the outside looking in on the money list. He is currently ranked 160th but a solid weekend could turn things around.
'This year has been a real battle for me,' said Brehaut. 'I feel like I've played better than I've scored or performed. It's been frustrating, this is my 32nd event which is way more than I want to play. I got a 10-year-old and 5-year-old at home and it's very difficult leaving. But I put myself in this position, so I got to try and work my way out of it.'
Brehaut birdied each of his first two holes and converted a 12-footer for birdie at the par-5 ninth to reach minus-7. The 41-year-old stumbled to a bogey at the 10th, but hit his second shot to 30 feet at the par-5 13th and ran home the putt for an eagle.
He tallied another birdie at the 15th and hit his second shot to 10 feet for a birdie and a round of 66.
Pernice started on the back side and ran off back-to-back birdies from the 12th to get to 8 under. He kept on cruising with a birdie at the 15th and made it two in a row with a birdie at the 16th.
The 45-year-old added a birdie at the first to move to 11 under, but found trouble with a bogey at the fourth, his first dropped shot of the tournament, en route to a round of 68.
First-round leader Jason Dufner carded a 70 to finish two shots off the pace at 9-under-par 135 along with Tom Lehman, Jerry Kelly, Bo Van Pelt and Joe Ogilvie. Hank Kuehne and David Frost followed at 8-under-par 136.
Ryan Moore shot a 69 to become the first amateur to make the cut at this event since Gary Pinns in 1980. Moore, who is trying to become the first person to win a PGA Tour event as an amateur since Phil Mickelson titled in Tucson in 1991, joined Brenden Pappas, Ben Crane, Blaine McCallister, Brett Quigley and Michael Allen at 7-under-par 137.
Defending champion Shigeki Maruyama was one shot further back in a group at 6-under-par 138.
The 36-hole cut fell at 3-under-par 141 with 71 players qualifying for the weekend. Among those who weren't as fortunate were course designer Davis Love III, John Daly, Jay Haas, Luke Donald and Jim Furyk.