America's Peterson trailed Pieters by two shots heading into the final round, but followed his course-record 64 on Saturday with 67, to close on 15 under par and edge out Pieters by one stroke.
Belgium's Pieters came agonisingly close to defending his title, losing the lead he had held overnight with just two holes to play. Pieters jetted 6,000 miles from Rio after finishing fourth at the Olympics in a bid to chase automatic qualification for September's Ryder Cup.
Back-to-back victories would have proved sufficient to ink his name onto Europe's team sheet, but now that chance has gone.
Englishman Matthew Fitzpatrick is now almost virtually assured of his place at the Ryder Cup however, after finishing fifth at 10 under par.