Ryan Howard added two hits and drove in three runs, while Ben Francisco slugged a solo homer and knocked in a pair for the Phillies, who snapped a three-game slide.
The 25-year-old Kendrick (5-3) surrendered 10 hits and three earned runs while fanning four and walking two to earn just his second win in seven starts.
Ryan Church finished with a trio of hits, including a homer, and Pedro Alvarez contributed a solo blast for the Pirates, who had won four of five coming in.
Paul Maholm (5-7) was battered in defeat for 10 hits and eight runs — seven earned — over three-plus frames.
The Phils, who scored in six of the first seven innings, tallied five times in the third to assume control.
Rollins kicked things off with a walk, followed by Shane Victorino’s infield single. Jayson Werth reached when Bucs’ shortstop Bobby Crosby booted a sure- fire double-play grounder then Howard singled home two runs for a 4-1 game.
Francisco’s groundout plated another run, and after a Wilson Valdez base hit, Cody Ransom singled home Francisco and Dane Sardinha doubled in Valdez for a 7-1 contest.
Werth’s RBI double in the fourth made it a seven-run edge for the visitors, and Rollins reached the left-field seats with two down in the fifth for a 10-1 game.
Church’s leadoff shot in the home fifth brought the Pirates within eight, but Francisco slugged a two-out homer for an 11-2 Phils’ edge.
Rollins then doubled home Kendrick, who doubled before him, to make it 12-2 in the seventh.
Pinch-hitter Ronny Cedeno had a run-scoring double in the eighth for Pittsburgh and Delwyn Young added an RBI single in the ninth, but Kendrick closed out his milestone victory by inducing a fielder’s choice grounder from Jose Tabata.
Victorino’s triple and Howard’s single staked the Phillies to a 2-0 lead in the first inning, then Alvarez hit his first career homer to halve the Pirates’ deficit in the second.
Kendrick improved to 4-0 in four career starts against the Pirates…Philadelphia hadn’t scored in double digits during a true road game since a 10-6 win at Milwaukee on May 16…Rollins’ homer was his 150th career blast…Prior to the contest, the Phillies selected Ransom’s contract from Triple-A Lehigh Valley, and designated utilityman Brian Bocock for assignment…Pittsburgh had gone just eight games without allowing 10-or-more runs, since a 14-4 loss at Oakland on June 25.