The Braves saw their lead in the National League East over second-place Philadelphia reduced to a single game.
Florida has won three in a row and inched within nine games of the Braves. The Marlins are eight games out of first place in the wild-card race.
Morrison tripled in a run in the first and scored on a double by Hanley Ramirez. Morrison led off the third with another triple and Ramirez drew a walk. Both runners scored on a double by Tracy.
Andrew Miller (1-0), making his second start since being called up, got his first win of the season and the 15th of his career, allowing a run on seven hits with six strikeouts over five innings.
Four relievers teamed to throw four hitless innings with five strikeouts.
Kenshin Kawakami (1-10) suffered the loss in his first start since June 26. He gave up five runs on five hits in three innings.