Pierre's run-scoring single in the fifth handed the Phils a 5-2 lead and Rollins' two-run homer in the next frame capped an outburst that widened their advantage to 8-3.
Chase Utley went 3-for-3 with an RBI and Domonic Brown added two hits, including a run-scoring single, as the Phillies claimed the opener of a three-game series and matched their season high in consecutive wins.
Roy Halladay (10-7) claimed the decision despite yielding five runs on seven hits over 6 1/3 innings, while Jonathan Papelbon secured the victory with his 33rd save.
Marlins starter Nathan Eovaldi (4-12) was touched for five runs on eight hits over four full innings.
Giancarlo Stanton homered and Justin Ruggiano added a pair of RBI singles for Miami.