Bugg, 25, had an eagle, six birdies and a bogey in the final round en route to a tournament-record 17-under 271 total on the Diamante Country Club.
'This is a lot of security,' said Bugg, who collected $81,000 for his first tour title. 'My schedule was pretty much mapped out with Monday qualifiers, but it turns out we don't have to do that anymore. We're done with that.'
Bugg is the 13th Monday qualifier to win a Buy.Com Tour event, and the first since Ben Crane in the 2000 Wichita Open.
Third-round leader Aaron Baddeley, who has twice won the Australian Open, shot 70 to finish two strokes back. Former PGA Tour players Tommy Tolles and Cliff Kresge closed with 67s to tie for fourth at 274.
Full-field scores from the Buy.Com Arkansas Classic