The 34-year-old survived a mid-round wobble to win by two strokes from fellow Americans Matt Every and John Huh after shooting a even-par round of 70 at TPC San Antonio on Sunday.
Back-to-back bogeys at 11 and 12 dropped Curtis back level with Every but after he and Huh faltered late on Curtis birdied the last to seal victory on nine under.
"It's been a tough couple of years," said Curtis, who had been playing on a limited status after his lean recent form.
Curtis had not won on the PGA Tour since the 2006 84 Lumber Classic but despite lack of recent success kept his nerve on Sunday.
He had set up his success after a bogey-free opening two rounds and never trailed on Sunday after starting with a four-stroke lead.
The jitters looked like settling in though when he dropped consecutive shots but Every, who was denied a first PGA Tour title after his course-record 63 on the opening day, bogeyed 15 to slip a stroke back alongside Huh.
Curtis made a clutch par putt on the 17th and when Every and Huh failed to birdie the last he reached the final green with two shots to seal victory.
He needed only one as he rolled in a 12-footer.
Defending champion Brendan Steele fired a flawless final-round 67 on Sunday to climb up the leaderboard and finish in a tie for fourth on five under with Bob Estes, Brian Gay and Charlie Wi.