'This has truly been an amazing week,' said Veazey. 'You could feel the excitement in the air all day. The people of Panama are great. The crowds were awesome. What more can you say?'
Camilo Villegas posted a 69 to finish one shot back alongside Shane Bertsch, Jon Mills and Jim McGovern at 7-under-par 273. Scott Sterling finished alone in sixth place at 5-under-par 275.
It wasn't easy for Veazey Sunday at Panama Golf Club. He struggled out of the gate with a double bogey at the par-4 second and from that point on he was in a battle to regain the top spot.
'It was a roller coaster day for me,' he said. 'I got off to a nightmare start and then my emotions were all over the place on the back nine. Someone was definitely smiling down on me today.'
Veazey recovered well with a birdie at the par-4 third and ran off three consecutive birdies from the par-3 sixth to make the turn in control at 10 under par.
The 39-year-old came back to the field, however, with back-to-back bogeys starting at the par-4 10th. He birdied the 12th, but gave that shot back with a bogey at the 13th.
Veazey fell back to 7 under with a bogey at the 16th and McGovern surged into the lead momentarily with birdies at 16 and 17. The tables turned for McGovern at the closing hole, however, and he bogeyed the last for a round of 68.
Veazey regained his composure and birdied the 17th en route to his first win since the 1999 Carolina Classic.
'This is by far the biggest accomplishment of my career,' said Veazey, who pocketed $94,500 for the win. 'I am getting to a point in my career where I need to start doing something. Hopefully this will be a break-out year for me.'
Chris Tidland, Steven Alker, Jason Schultz and former U.S. Amateur champion Ricky Barnes tied for seventh at 4-under-par 276.