Hellickson (1-1) notched his first victory over the season, allowing three hits and one walk over seven scoreless frames. The right-hander struck out six.
Matt Joyce provided the game's only run with a second-inning homer.
The Athletics' Jarrod Parker (0-3) absorbed the hard-luck loss despite limiting Tampa Bay to just the one run on six hits and two walks over 6 1/3 innings. He fanned five.