Higgo, who led by two shots heading into the final round in Mississippi, battled bravely but costly errors on the back nine proved decisive as Fisk stormed home with a brilliant eight-under 64 to seal his maiden PGA Tour triumph.
The South African's closing 68 left him on 22 under - two strokes behind Fisk - after an enthralling head-to-head battle that swung dramatically over the final few holes at the Country Club of Jackson.
Higgo looked in control early on before faltering with back-to-back bogeys at the 10th and 11th. The South African briefly recovered with three consecutive birdies from the 13th to the 15th, pulling level once more.
Fisk, though, struck a decisive blow on the 16th, sinking a stunning 41-foot birdie putt to move ahead. Higgo answered immediately with a clutch 11-footer of his own, setting up a tense finish.
At the par-four 17th, Fisk stiffed his approach to three feet — and when Higgo missed a near-identical birdie chance, Fisk converted to reclaim the lead. Another pinpoint iron at the last left him a tap-in birdie to seal victory, the $1.08 million winner's cheque, and a PGA Tour exemption through 2027.
"I came out today with an attitude that nothing was going to stop me from what I wanted, no matter what happened, no matter what shots I hit," Fisk said afterwards.
"I just felt like I'd be standing right here, right now before today started," Fisk added, attributing his win to "self-belief and grit."
"I know I'm good enough -- I thought I could do it," he said. "It's a lifelong dream. Honestly, sometimes you doubt yourself, but like I said, I knew I could do it. And to have some job security is pretty nice. It's been a long, hard year."
Denmark's Rasmus Hojgaard shared third place on 19 under alongside Americans Vince Whaley and Danny Walker, finishing one shot ahead of a trio in sixth that included South Africa's Christiaan Bezuidenhout.