Palmer earned his first win on the Nationwide Tour in only his second start. His four-day total of 271 matched Peter O'Malley's tournament record from last year.
'It was a real struggle to get here and at the moment I just can't tell you what it means to win,' said Palmer, who earned $110,520 for the victory. 'I've had to really work hard to get where I am now and to win in only my second tournament, it's too tough to say how I feel right now.'
American Kevin Johnson finished alone in third place at 12-under-par 276, followed by David Branshaw, who shot a final-round 67 to come in at 10-under par for the championship.
Stolz collected a pair of birdies at two and six to get within one shot of Palmer's lead. Palmer, who collected one birdie and one bogey in the same span, took command of the tournament at the eighth.
Palmer holed out his second shot for an eagle-2 at No. 8 and went three ahead. Stolz birdied the 11th and 12th holes to get within one of the lead and both players birdied the 14th to keep the margin at one.
Palmer birdied the 15th hole to go ahead by two and when Stolz bogeyed the last, Palmer walked off with a three-shot victory.
'Andre and Kevin were playing real well today and that made it hard on me,' said Palmer, who took the lead in the tournament after a course-record 63 on Friday. 'I knew there was pressure, but going into the back nine I knew I was putting well and that kept my fire going.'
Stolz posted a 4-under 68 for the second-place finish. He tied for sixth place last week at the Jacob's Creek Open Championship. Johnson shot a final-round 67.
Nick O'Hern finished alone in fifth place at 9-under-par 279, followed by O'Malley (71), David Morland IV (69) and Chris Downes (69). The trio shared sixth at minus-8.
Jess Daley (68), Rick Price (70) and Kyle Thompson (69) tied for ninth at 7-under-par 281.