The victory capped a remarkable turnaround for Holmes, who won for the third time in his career.
He was diagnosed in 2011 with structural defects in the cerebellum known as Chiara malformations, and he had surgery twice once to remove a piece of his skull that he still keeps at home, another because of an allergic reaction to the adhesive on the titanium plate at the base of his skull.
Then, he injured his elbow by hitting too many balls in an attempt to return from the brain surgery. He didn't bother having surgery on his elbow until last year, when he was sidelined by a broken ankle and couldn't play, anyway.
Only last week, Holmes earned enough money to keep his card for the rest of the year from a medical extension. Now, he's headed to The Players Championship next week for the richest prize in golf, and more importantly, secured a spot in the PGA Championship this summer in his native Kentucky.
"It's been a long journey for me," Holmes said. "I've had some ups and downs. It's a great feeling to be out there and to get one done."
His only other victories were in the Phoenix Open in 2006 and 2008.
Furyk was watching on TV in the locker room when Holmes knocked in the bogey putt to finish at 14-under 274.
Martin Flores, in his first time playing in the last group, fell too far back with a three-putt bogey on the 13th. He made bogey on the 18th for a 72 and was third, the best finish of his PGA Tour career. Bohn also bogeyed the 18th for a 70 to finish fourth.
Mickelson matched his highest final round on the PGA Tour since The Barclays in 2012.
After six runner-up finishes in her previous 16 tournaments, Stacy Lewis took control in the final round of the North Texas LPGA Shootout in Irving, Texas, shooting a 7-under 64 for a six-stroke victory over Meena Lee. With consecutive birdies at the end, Lewis finished at 16-under 268 and with the LPGA Tour's largest margin of victory since Jiyai Shin won the 2012 Women's British Open by nine.
It was the ninth career LPGA Tour victory for Lewis, and her first since August in the Women's British Open.
Bernhard Langer won the Champions Tour's Insperity Invitational for the third time, closing with a 1-under 71 for a one-stroke victory over Fred Couples at The Woodlands, Texas. Langer finished at 11-under 205 to become the 10th 20-time winner on the 50-and-over tour.