Cloyd (1-1), an 18th-round 2008 Phillies draft choice out of Nebraska-Omaha, struck out nine while yielding one run on four hits. The right-hander didn't allow a walk in his second big-league appearance.
Justin De Fratus tossed a scoreless eighth and Phillippe Aumont collected his first major league save despite surrendering a run in the ninth as the Phils took the opener of a three-game set.
Johnny Cueto (17-7) absorbed the loss for the National League Central-leading Reds, giving up four runs on eight hits over seven full innings.
Jay Bruce homered and added a run-scoring single for for Cincinnati.