Veazey and Garrett Willis needed two extra holes to decide the tournament, with Veazey finally ending things at Panama Golf Club's par-4 10th hole.
With the victory, Veazey moved into a 17-way tie for seventh place on the Nationwide Tour's all-time wins list. Only Matt Gogel, Jason Gore and Sean Murphy ' with six wins apiece ' and Pat Bates, Chris Couch and Chris Smith ' with five ' have more titles on the circuit.
Veazey, who also won the 2005 Panama Championship, shot a 1-under 69 in the final round.
Willis, a former PGA Tour winner who was seeking his second Nationwide Tour victory, birdied four of the last six holes in regulation to shoot a 4-under 66.
The players ended regulation tied at 7-under 273, two shots in front of Jeff Gove (70).
Veazey, the third-round leader, kept his spot on top of the leaderboard until he made a bogey at the 14th, his second in five holes. The mistake gave Willis, already in the clubhouse, the outright lead.
Veazey said he didn't realize he was behind until he reached the 17th hole.
'Coincidentally, I was in the same situation on the same hole in final round when I won here in 2005,' said Veazey, who was in a five-way tie for the lead four years ago until he birdied the 17th.
On Sunday, the 43-year-old veteran didn't make his key birdie until the 18th hole, where he rolled in an 8-foot putt to force the playoff.
Both players made routine pars on the first extra hole, the 18th, before heading to the par-4 10th.
While Willis struggled to find the green ' it took him four shots ' Veazey knocked his approach to the middle of the surface and two-putted from 20 feet for the win.
He became just the eighth player in Nationwide Tour history to win the same event twice.
'I wish I could play 20 tournaments here,' said Veazey.
Henrik Bjornstad (69) and Jim Herman (71) tied for fourth place at 4-under 276, while Rich Barcelo (68), Bryan DeCorso (70), Rafael Gomez (71) and Len Mattiace (72) shared sixth at 3-under 277.
The tournament marked the beginning of the Nationwide Tour's 20th season.