Kendrick (5-9) notched his seventh straight victory against the Marlins, handcuffing them on five hits without issuing a walk. The right-hander allowed only one runner to get as far as third while striking out six.
Josh Lindblom tossed a scoreless eighth and Jonathan Papelbon racked up his 26th save for the Phillies, who clinched their three-game series.
Rollins led off the first inning with a solo homer off Josh Johnson (7-9) to provide the contest's only scoring.
Johnson (7-9) absorbed the hard-luck loss for the Marlins, who suffered their third consecutive shutout. The right-hander allowed only three hits over eight frames, issuing one walk and striking out seven.
Miami set a club record by going 27 straight innings without scoring a run.