Sutterfield finished 36 holes at 5-under-par 139. Mario Tiziani stands at 4-under par through 15 holes. Peter Wilson posted a 2-under 70 to finish two shots off the pace at 3-under-par 141.
Frost in the morning on the Fazio Foothills Course at Barton Creek Resort delayed the start of play on Friday for two hours, ultimately leading to the suspension of the second round.
Sutterfield dropped a shot with a bogey at the third but he recovered with a birdie at the par-5 eighth. He found trouble with a bogey at the very next hole, however, and stumbled again with a bogey at the 10th.
The 35-year-old redeemed himself down the stretch starting with an eagle at the short par-4 12th before picking up a birdie at the 13th.
Sutterfield added a birdie at the par-5 15th and closed with a birdie at the par-5 last to take the lead in the clubhouse despite sending his tee shot into the trees.
'I got a big break on that final hole and instead of making a six, I ended up with a four,' said Sutterfield. 'As soon as I hit the tee shot, I was thinking bogey. Sometimes you have to take advantage of those situations, and I was able to do that.'
Rob McMillian had completed 15 holes at 3-under par before the round was called. Chris Wall was also at minus-three through 14 holes with Ryan Miller rounding out the group at 3 under through nine holes.
Jason Schultz, Rodney Butcher, Keith Fergus and Kris Mikkelsen are in the clubhouse at 2-under-par 142.