Marco Scutaro's three-run homer in the top of the fifth erased a 4-3 Toronto deficit.
Rolen brought home a run with a bases-loaded walk in the seventh.
The winner was reliever Shawn Camp (3-1).
Tampa Bay's Evan Longoria and Carlos Pena hit back-back solo homers in the bottom of the third.
Carl Crawford knocked in one run and scored one on a second-inning wild pitch by Toronto starter John Parrish.
Six players had one hit for the Rays, who won the first two games following their seven-game losing streak.
Losing pitcher Edwin Jackson (5-7) surrendered six earned runs and eight hits in 4 1/3 innings.
Celebrity Families of 2014 [PHOTOS]