Hellickson (11-8) gave up six hits, fanned five and issued only one walk. Joel Peralta tossed the ninth.
Evan Longoria finished with a home run and four RBI, while Johnny Damon and Ben Zobrist collected three hits apiece for the Rays, who have taken the first two games of this series and four in a row overall.
Charlie Furbush (3-5) gave up five runs on eight hits in just three innings of work. He struck out two and walked one.