Camilo Villegas, who held the top spot heading into the weekend, struggled with a 71 to finish two shots off the pace at 6-under-par 204. Former U.S. Amateur champion Ricky Barnes followed at 5-under-par 205 along with Ryan Hietala and Jim McGovern.
Veazey was three shots back Saturday at Panama Golf Club and picked up his first birdie of the day at the par-4 second. He kept on rolling with a birdie at the par-5 fourth and reached 7 under with a birdie at the par-3 second.
The strong start pushed Veazey to the top of the leaderboard, but the 39-year-old could not pull away from his competitors with a string of 11 consecutive pars.
'I didn't make a bogey today and that was the key to my round,' said Veazey. 'I played steady all day and once again made some putts. The putter has gotten me to this position this week.'
Veazey's steady play concluded with a birdie at the par-4 18th and a slim advantage with one round to play.
'I want to go out tomorrow and play every shot the best I can and when it is over we'll add them all up,' said Veazey, who is seeking his third career victory on the Nationwide Tour and first since the 1999 Carolina Classic. 'This golf course presents a new challenge every day. So I've got a lot of work ahead of me tomorrow.'
Mills tallied a birdie and a bogey over his first nine holes to make the turn at 5 under. The Canadian collected two straight birdies from the 10th and parred his way in for a round of 68.
Bertsch had an up-and-down front nine with three bogeys and a pair of birdies. He countered on the inward half with a trio of birdies for a 68 of his own.
Alker carded a round of 69 that featured three birdies and two bogeys.
Bryce Molder shot a 65 to move into a tie for ninth place along with Chris Couch, Bubba Dickerson, Chris Tidland, Jason Schultz and Robin Freeman at 3-under-par 207.