Veazey, the 2005 champion, finished three rounds of the Nationwide Tour's season-opener at 6-under-par 204.
Len Mattiace, a two-time PGA Tour winner, fired a 6-under 64 to climb from a tie for 31st place into a share of second at 5-under 205. Jim Herman, Camilo Benedetti and Jeff Gove all shot 68s to join him there.
Second-round leader Rafael Gomez had a 1-over 71 and fell into a tie for sixth place with Chris Smith (68) and Esteban Toledo (68) at 4-under 206.
The wind was down compared to the first two days of the tournament, and players took full advantage of the improved scoring conditions.
But Veazey, a 43-year-old veteran with three career Nationwide Tour wins, wasn't excited about the prospect of the wind remaining light for Sunday's final round.
'I hope the wind comes up a bit tomorrow ' it benefits me,' he said. 'I keep the ball down and have a lot of experience playing in the wind.'
Beginning the round one shot off Gomez's lead, Veazey didn't make his first birdie until the fourth hole. He collected one more birdie on the front nine ' at No. 7 ' and made the turn at 6 under.
Veazey stumbled to a bogey at the 10th, his only dropped shot of the third round, but got the stroke back with a birdie at the 17th, taking the overnight lead.
'I didn't hit the ball quite as well today, but I made some key putts when I had to, like a 6-footer for par on 17,' said Veazey, whose last Nationwide Tour win came at this event in '05.
There were 25 players within five shots of Veazey's lead heading into the final round ' not an uncommon occurrence for the tour's Panama stop.
'The scores are always very tight at this event,' said Mattiace. 'I started six strokes back today and finished just one shot behind the leader ' anything can happen over the weekend.'
The tournament marks the beginning of the Nationwide Tour's 20th season.