Albert Pujols, obtained by the Angels in the highlight free-agent signing of the off-season, extended the worst drought of his career to 0-for-19. He went hitless in three at-bats with a walk.
Tampa Bay won its fourth in a row, getting a five strikeout performance from Hellickson (3-0).
With the tying run on first, Rodney got pinch-hitter Alberto Callaspo on a fly ball to left to end the game.
Zobrist opened the scoring with a solo homer in the third and Jeff Keppinger had an RBI double later in that inning. Brandon Allen drew a bases-loaded walk in the eighth for what turned out to be the winning run.
Vernon Wells hit a fourth-inning homer for the Angels.
C.J. Wilson (2-2) struck out 11 over seven innings, but suffered the hard-luck loss while giving up two runs on six hits.