"I'm really proud of myself, hanging in there today," said the 25-year-old Bezuidenhout, who arrived in Sotogrande in good form following a tie for third at last week's BMW International Open in Munich.
After three rounds in the 60s, Bezuidenhout started Sunday's final round five shots clear of Spanish world number 11 Jon Rahm.
Birdies at the first two holes seemed to have set up a victory procession for Bezuidenhout, but he promptly bogeyed four of the next five and his lead was down to three.
The pivotal moment came at the eighth hole, where he holed a clutch 10-foot putt to save par and stem the bleeding.
"I went through a stuff stretch (but the) great save on eight kept the momentum on my side and bounced back with three birdies in a row," Bezuidenhout said.
"That settled me down nicely. I knew I just had to keep going and hit greens."
He finished at 10-under 274.
Rahm battled to a 72 and a share of second place with fellow Spaniards Alvaro Quiros (66), Adri Arnaus (69), Eduardo de la Riva (69) and Frenchman Mike Lorenzo-Vera (68).
Arnaus and Lorenzo-Vera also punched tickets to the July 18-21 Open at Royal Portrush.
Tournament host Sergio Garcia finished another shot back, alone in seventh.
(Reporting by Andrew Both in Cary, North Carolina, editing by Pritha Sarkar)
