Zobrist ended with three hits and four runs scored, while Elliot Johnson went 4-for-5 with three RBI for the Rays, who clinched their three-game series at Marlins Park.
Jose Molina drove in three runs as Tampa Bay retained its half-game lead in the American League East.
Matt Moore (3-5) struck out nine over six innings to earn the victory, allowing four runs on five hits while walking two.
Marlins starter Carlos Zambrano (4-4) lasted only 2 1/3 innings, coughing up seven runs on five hits and three walks.
Justin Ruggiano blasted a three-run homer for the Marlins, who dropped their fifth straight.
Celebrity Families of 2014 [PHOTOS]