The pair were joint leaders at five-under following the third round, with several other contenders within striking distance at the 2018 Ryder Cup venue.
Yet Northern Ireland's McDowell, the 2010 U.S Open champion, and Sterne both birdied two of their first six holes to ensure they were in prime position to keep their rivals at a distance.
McDowell bogeyed the par-four seventh, only his fourth of the week, but picked himself up to birdie the ninth and 10th as Sterne began to falter.
The South African fell away after the turn, bogeying the 12th, 16th and 17th.
McDowell hit a superb birdie on the 17th to add a final flourish and add to his wins at the RBC Heritage in South Carolina and the Volvo World Match Play Championship in Bulgaria.
He ended with a four-under 67 and winning total of nine-under 275.
McDowell, who missed the cut at last week's Irish Open in what has been a year of fluctuating results for the Ryder Cup stalwart, moved to second behind Justin Rose in the Race to Dubai rankings.
"It's very special after the last couple of months," McDowell told the European Tour website (www.europeantour.com).
"It's been a bit of a battle. It's been a funny year. My game has not felt far away most weeks but I have missed a lot more cuts than normal and missing cuts hurts.
"It certainly motivated me a lot the last few weeks. The U.S. Open was a tough one to take and missing the cut in Ireland last week.
"It made me more hungry to want to be in positions like I was this afternoon."
Sterne, also a winner on the tour in 2013, finished the round on even par and five-under for the tournament, while Spain's Eduardo de la Riva and England's Graeme Storm were tied for third a shot further back.