A deft chip at the par-five 18th set a up a tap-in birdie and a two-under-par 68 at East Lake.
At 15 under par, Koepka will head into the final round on Sunday afternoon with the narrowest of leads over fellow American Xander Schauffele (67) and Northern Irishman Rory McIlroy (68).
Englishman Paul Casey (68) and American Justin Thomas (71) trail by four shots, Thomas left reeling by a triple-bogey at the 16th hole.
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The third round was completed on Sunday morning after being suspended on Saturday afternoon due to a thunderstorm.
Six spectators were subsequently injured after a lightning bolt struck a tree on the course.
Five were taken to hospital and all have now been released, the PGA Tour said in a statement.
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