The Marlins suffered only their third loss in 11 games, managing just three hits off three pitchers.
It was a 1-1 contest heading into the third, but Matt Carpenter and Jon Jay singled to open the inning and Holliday followed with his double that brought home Carpenter.
Allen Craig delivered a run with a sacrifice fly and a double from Matt Adams brought home Holliday with the final run of the game.
Mujica recorded his 22nd save one night after suffering his first blown save opportunity of the season in a loss to the Los Angeles Angels.
Jacob Turner (2-1) took the loss, surrendering four runs on seven hits in six innings.