The 55-year-old Weibring finished at 9-under 271, edging Fred Funk, who closed with a 66 for 272.
Weibring, a five-time Champions Tour winner, collected $390,000.
"I didn't play my best today, but I hung in there," Weibring said.
Weibring sank a 9-foot putt to save par on the next-to-last hole, a putt he didn't expect to go in.
"I guess that's what happens when it's your day," he said.
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