The bulk of the field is made up of players in the top 75 on the Web.com Tour money list and Nos. 126-200 in the PGA Tour's FedEx Cup standings. The top 25 on the Web.com money list are assured PGA Tour cards, while the other players are fighting for 25 additional cards through earnings in the four-event series.
Svoboda has already wrapped up a PGA Tour card by finishing 25th on the Web.com money list. Peterson was 30th on the Web.com money list.
Peterson had five back-nine birdies to shoot 5-under 67 and match Svoboda at 10-under 206 at River Run.
"I just stayed out there, and my caddie told me just to stay patient," Peterson, the 2011 NCAA champion at LSU, said. "I don't usually do a good job of that, but I did it today and it came around for me on the back.
"I was hitting good shots on the front and a bunch were in that 10- to 12-foot range. I kept hitting it close and finally hit it close enough where it was hard to miss. I can make it from 3 feet, I just couldn't make it from 10 feet today."
Svoboda birdied the final two holes for a 69. The former St. John's player won the Web.com Tour's Price Cutter Charity Championship last month.
"Anywhere around the lead is nice," Svoboda said. "It was really nice to finish with those two birdies."
He made a 20-foot putt on the par-3 17th hole and an 18-footer after laying up on the par-5 18th.
"It was between a 3-wood and a hybrid for me," Svoboda said. "I had 240 to the hole and hitting a 3-wood off a downhill lie just wasn't good for me. I wasn't sure I could get that one up in the air off that lie."
"On this course you'd rather be ahead," Matteson said. "This is not one where you can shoot 9- or 10-under and catch back up. This is kind of a 'steady Eddie' course. It's just very difficult to shoot a low number."
Ricky Barnes was 7 under along with Brendon Todd, Ben Martin, Vaughn Taylor, Hudson Swafford and Will MacKenzie. Todd had a 68, Barnes and Martin shot 69, Taylor had a 70, Swafford a 71, and MacKenzie a 72.