Then, with Maxwell at third and Randy Choate on the mound, it seemed the rally would come to an end when Brian Bogusevic lofted a routine fly ball to left. But the ball popped out of Morrison's glove, allowing the go-ahead run to score.
Brett Myers made the lead hold up with a 1-2-3 bottom of the ninth, earning his second save of the year and snapping the Astros' three-game skid.
Rhiner Cruz (1-0) earned his first major league win with scoreless innings of one-hit ball in relief.
Morrison had two RBI for the Marlins.
Carlos Zambrano started for Miami and surrendered just one run on four hits while issuing six walks.