The 39-year-old Furyk, playing in the event for the seventh time, closed with his second-consecutive 5-under-par 67 to finish at 13-under 275 and earned $1.35 million. McDowell, who received a late entry into the tournament due to an injury to tournament host Tiger Woods, also birdied the 18th hole to shoot 70 and claimed second place.
Lee Westwood (70) and Padraig Harrington (70) tied for third.
It was a satisfying win for Furyk, who hadn't won anywhere in 28 months.
"It bothered me," said Furyk, who made only two bogeys in the last 44 holes. "I'd be lying if I said otherwise. That's your goal every year, to go out there and win, and I haven't been able to do that in two full seasons on Tour. Hopefully, this will be a stepping stone."
With eight players lurking within three shots of co-leaders McDowell and Y.E. Yang after three rounds, Furyk knew he would have to play aggressive golf to overtake them.
"I knew I'd have to fire a good number," he said.
Furyk took the lead on the back nine and retained it with a long par save at the par-3 17th hole, where he missed the green with an 8-iron.
"I'm very thankful that putt went in," said Furyk. "You gotta get a little a lucky. That's how you win golf tournaments."
Proceeds from the tournament benefit the Tiger Woods Foundation.