Hunter Pence and Shane Victorino contributed RBI singles during the four-run first, during which the Phillies scored on fielding errors by Pirates third baseman Pedro Alvarez and right fielder Jose Tabata.
Rollins' shot in the fourth gave Philadelphia a 7-2 lead and the Phillies went on to take the opener of a four-game series.
Carlos Ruiz went 3-for-5 with three runs scored in the victory.
Joe Blanton (7-6) earned the win, allowing three runs (two earned) on seven hits over seven innings. The right-hander struck out eight while issuing only one walk.
Bucs starter Jeff Karstens (0-2) came off the disabled list to yield seven runs (six earned) on 11 hits in a five-inning effort.
Tabata knocked a solo homer for second-place Pittsburgh, which fell two games behind National League East-leading Cincinnati.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys