He added birdies on Nos. 5 and 6, then recorded three more on the back nine to polish off the win and the record. He finished 19-under 194 for the tournament.
"My mind this week was just kind of -- I (wasn't) worrying about a bunch of the minutiae out there," Flesch said. "I just was playing golf.
"Hitting shots that end up where you kind of are aiming has a lot to do with it, too, but it was nice to actually be in the competition this week and feel like my shots meant something, and I was just dialed in, and I was focused."
Flesch came into the day having to catch up to co-leader Kevin Sutherland, the only bogey-free player through two rounds.
Sutherland scored two birdies on the front nine Sunday before running into trouble with a bogey on No. 13. He rallied with three birdies over the final five holes, but he couldn't keep up with Flesch's hot pace, finishing in second place (16 under) with a final-round 67.
The other Saturday co-leader, Y.E. Yang of South Korea, fell into a tie for third (13 under) with his 1-under 70. He was tied with Brett Quigley, who shot a 3-under 68.
Three golfers tied for fifth at 12 under. Scotland's Colin Montgomerie shot a 5-under 66, David Toms recorded a 4-under 67 and Ken Duke pocketed a 1-under 70.
Richard Green of Australia (65) and Tim O'Neal (67) tied for eighth at 11 under.