Cincinnati, owner of the second-best record in the majors behind Washington, had a three-game winning streak snapped in the opener of a three-game series.
Turner (2-3) gave up two hits -- a two-out double in the second and a one-out single in the fourth. He walked two and struck out three during a seven-inning effort that included 101 pitches.
Heath Bell and Steve Cishek each worked an inning to complete the shutout.
Justin Ruggiano doubled in Miami's first run in the third, Greg Dobbs hit a solo homer in the fourth and Carlos Lee added a two-run single in the fifth. The Marlins had lost their previous three outings.
The loss went to Bronson Arroyo (12-8), who gave up four runs on nine hits in six innings.