McDowell finished at 13-under 271, two shots ahead of James Kingston, who closed with a 66.
The 28-year-old McDowell, who will play in the British Open this week, has won twice this season.
"It really was a tough weekend of golf with such a stacked field," McDowell said. "This is a massive relief."
World No. 2 Phil Mickelson carded a 2-over 73 and ended up 12 shots back.
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