"It's hard to believe," said Mize, who graduated from Augusta Prep and now lives in Columbus, Ga.
The 51-year-old Mize, the 1987 Masters Tournament champion, had an eagle, seven birdies and a bogey in the final round to finish at 17-under 199.
He won $270,00 and moved from 26th to 10th on the tour's money list, with $551,302.
"Any time I had a complacent thought I told myself, 'Keep making birdies,' " said Mize, a winner for the first time since the PGA Tour's 1993 Buick Open.
The win came in Mize's 36th start on the 50-over circuit. Coming in, he had 14 top-10 finishes, with his best finish being a runner-up in the 2009 Senior PGA Championship.
"You have doubt and you have to replace the doubt with belief in your ability," he said. "I just said, 'Continue to believe in yourself. You've put in the work and trust it.' Doubts are no fun."
Cook shot 68, but missed a 25-foot birdie putt on No. 18 that would have forced a playoff with Mize, who then able to let his feelings go.
"I was holding back some emotion," he admitted. "I teared up a little bit. It's been a long time. Once it happened, it was hard to keep that emotion back."
Corey Pavin (67) and Dan Forsman (65) finished three behind Mize, and Fred Couples (68) was among a group of five players four shot back of Mize.
"Larry played an unbelievable round," Couples said. "He just kept going and going so that was nice to see."