Haas fired a 7-under 65 on Sunday to end the tournament at 16-under-par 200, two strokes better than overnight leader Dana Quigley, who shot a 70 in his final round.
The 51-year-old Haas had twice been a runner-up on the Champions Tour, with both of those finishes coming last year. And he hadn't placed better than a tie for ninth on any tour in 2005.
But three scores in the 60s -- and eight birdies in his final round -- had the father of five tasting victory for the first time since winning the H.E.B Texas Open on the PGA Tour in 1993.
'I played awfully well all three days,' said Haas, who collected $240,000 for the win. 'It was a great feeling to win again. Somebody told me it was 300 or so (tournaments) since I won, but I never thought about it.
'Not playing well on the Champions Tour was disappointing to me.'
Haas, who began the day in a tie for third place at nine-under, quickly moved further into red numbers with three birdies on his first seven holes, including a pair of two-putt birdies at the par-five fourth and seventh holes.
He dropped a shot at the par-3 ninth when he three-putted from the fringe and made the turn at minus-11. But Haas got two strokes back with consecutive birdies at 12 and 13.
Three straight birdies from the 16th then helped Haas keep ahead of Quigley and Roberts, who were playing behind him in the final group. Haas drained putts of 24 and 30 feet on the last two holes.
'I had to calm down after the birdie at number 17 because I was looking ahead and thinking birdie at number 18,' Haas acknowledged.
'My whole game hasn't been sharp this year, but this week it was. I had a very good ball-striking week.'
Roberts, who trailed Quigley by one stroke overnight, quickly assumed the lead by playing his first five holes at 3 under while Quigley was even-par over the same stretch. But Roberts stumbled to a triple-bogey at the par-4 sixth and managed just two more birdies after that.
'The birdies were out there and I just didn't convert,' said Roberts.
Quigley, whose bogey at No. 2 was his first in 32 holes, made just two birdies on his final 13 holes, including one at 18 that secured him second place.
'I didn't have it today,' he said. 'I tried to talk myself into being more aggressive, but I didn't.'
Seven players tied for fourth place at 11 under: John Harris (66); Don Pooley (66); Jim Thorpe (67); Jerry Pate (67); Tom Wargo (68); Craig Stadler (68); and Tom McKnight (70).