SAN ANTONIO, March 30, 2014 (AFP) - The 30-year-old Bowditch tapped in a short bogey putt on the par-five 18th to seal the win over runners-up Will MacKenzie and Daniel Summerhays.
The victory earns him a trip to the Masters where his Aussie compatriot Adam Scott is the defending champion.
"I am over the moon. I can't believe it," said Bowditch. "Just happened to be my week I guess."
Bowditch, who is ranked 339th in the world, had a roller-coaster round Sunday that included that bogey on 18 as he finished with an eight-under 280 total at the TPC San Antonio.
Bowditch entered the fourth round with a three-shot cushion over Matt Kuchar and Andrew Loupe.
The Newcastle native needed all of it as his Sunday round included two birdies, four bogeys and one double bogey.
Bowditch's final-round score was the highest by a US tour winner since Vijay Singh at the 2004 PGA Championship, but the field averaged 73.8 strokes in the blustery weather.
MacKenzie (70) and Summerhays (71) shared second place at seven-under 282, while Kuchar and Loupe shot matching three-over 75s to share fourth on six-under 282.
Zach Johnson (72), Jim Furyk (71), Jerry Kelly (71) and Brendon Todd (68) shared sixth at five-under.
Bowditch has less than a handful of international wins, coming off a distinguished amateur career.
As a pro, his time has mainly been spent bouncing back and forth between the PGA Tour and the developmental Web.com Tour.
Before this win, he had just two top 10 finishes in America. He had never even led a round of a PGA Tour event until this week.
Part of his trouble has been that Bowditch has had a long struggle with severe depression.
He is a leading spokesman for the Australian non-profit group beyondblue. The Melbourne-based organisation promotes awareness of depression and has also been speaking out in support of Olympic swimmer Ian Thorpe, who was recently admitted to hospital suffering from depression.
Bowditch -- who was congratulated near the 18th green by Australians John Senden, Aaron Baddeley and Scott Gardiner, said the positive people he surrounded himself with this week helped him battle through the rough patches.
"I've got a great supporting team," Bowditch said. "I drew on some of my experience and got some advice from different people."
Leading final-round scores on Sunday in the $6.2 million (4.5 million euros) US PGA Tour Texas Open (USA unless noted):
280 - Steven Bowditch (AUS) 69-67-68-76
281 - Will MacKenzie 69-72-70-70, Daniel Summerhays 72-68-70-71
282 - Matt Kuchar 70-72-65-75, Andrew Loupe 67-70-70-75
283 - Brendon Todd 71-76-68-68, Jerry Kelly 71-71-70-71, Jim Furyk 70-74-68-71, Zach Johnson 70-71-70-72
284 - Jordan Spieth 75-70-68-71
285 - Charley Hoffman 70-75-70-70, Geoff Ogilvy (AUS) 74-69-69-73, Pat Perez 68-71-69-77, Kevin Na 70-70-69-76
286 - Justin Hicks 69-73-72-72
287 - Noh Seung-Yul (KOR) 69-76-71-71, Michael Thompson 70-75-71-71, Brian Harman 70-72-75-70, James Hahn 71-70-76-70, Martin Flores 71-71-73-72, Wes Roach 75-66-72-74, Freddie Jacobson (SWE) 70-70-73-74, Carl Pettersson (SWE) 70-73-71-73, Jimmy Walker 76-71-71-69, Stephen Ames (CAN) 74-71-68-74
288 - Johnson Wagner 73-73-71-71, Russell Knox (SCO) 74-70-71-73, Bo Van Pelt 69-73-71-75, Andrew Svoboda 73-73-67-75, Chad Collins 71-66-73-78