Morton (1-1), who underwent "Tommy John" elbow ligament replacement last year, earned his initial victory five days after marking his season debut with a loss to San Francisco.
The right-hander stymied the Reds on three hits and didn't issue a walk en route to the decision. He struck out two.
Pedro Alvarez provided a two-run double in the first inning while Russell Martin and Starlin Marte each added an RBI for Pittsburgh, which notched a second straight win in its four-game series against division rival Cincinnati.
Reds starter Mat Latos (6-1) absorbed his first setback of the season, coughing up three runs on three hits over five innings.
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