Blixt came into the final round down by four strokes to overnight leader Johnson Wagner and had to wait out a 3-hour, 10-minute weather delay before beginning his round.
But then he took off, logging three birdies on the front nine. After bogeying 11 and 13 and notching a birdie in between, he clinched the title with a birdie on 16 with a 9-foot putt, finishing at 13-under 267.
It was the second career PGA Tour victory for the Swede, who gained a berth in next month's British Open and the 2014 Masters with the triumph.
Celebrity Families of 2014 [PHOTOS]