The American shot a three-under-par 69 in his final round to finish on 16-under for the tournament, just ahead of playing partner Pieters.
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It is the second time that Fowler, 27, has won on the European Tour following his victory at the Aberdeen Asset Management Scottish Open last summer.
Pieters would have forced a playoff with an eagle on the par-five 18th, but his putt just slid by as Fowler only made par.
Two of the five players above Fowler in the world rankings, Rory McIlroy and Henrik Stenson, finished in a tie for third on 14-under, while world number one Jordan Spieth was one of six players tied-fifth at 11-under.