McDowell was 2-down to Thongchai Jaidee after four holes in Sunday's Match Play final, an event on the European Tour schedule, but posted three birdies in a four-hole span over Nos. 12-15 in taking a 2-and-1 victory.
It was his first European Tour win since October 2010. He won the PGA Tour's RBC Heritage in April. Sunday's victory lifts him from eighth to seventh in the rankings in a trading of places with Louis Oosthuizen.
The week's other winners were Bae Sang-moon at the HP Bryan Nelson Championship for his first PGA Tour win and Peter Uihlein at the European Tour's Madeira Islands Open for his first professional title. Bae goes from 106th to No. 64 in the rankings while Uihlein is up 99 spots to 147th.