Peterson completed a 15-under-par victory ahead of Pieters, who had held a two-stroke lead overnight, with Britons David Howell and Ryan Evans joint third on minus 11.
The left-handed American crowned a fine weekend in which he added a five-under 67 in the final round to his course record 64 on Saturday with a birdie on the final hole.
"This is the best feeling in the world," Peterson told the European Tour website (www.europeantour.com). "My team and I have put in so much hard work and long hours by everybody and I'm just so happy.
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"We had this as a goal this year and to be able to accomplish it means so much," added the 24-year-old.
The result ended Pieters' hopes of taking an automatic place on Europe's Ryder Cup team since he needed a victory in Prague and also next weekend in Denmark, the last points-counting tournament.
Englishman Matthew Fitzpatrick, on the other hand, made almost certain of taking the final automatic spot in Europe's Ryder Cup team by finishing fifth on 10 under.
The United States hosts the Ryder Cup at Hazeltine in Minnesota from Sept. 27 to Oct. 2 looking to wrest the trophy back from Europe.
(Writing by Rex Gowar; Editing by Alison Williams)
