The Rays pushed across three runs in the sixth to take command of the contest. Diamondbacks starter Ian Kennedy (3-6) walked Matt Joyce, Jason Bartlett and B.J. Upton to load the bases, and Rodriguez made him pay with the key hit.
Carlos Pena followed with an RBI groundout and Bartlett drove in a pair to help Tampa Bay bounce back from being no-hit Friday for the second time this year.
David Price (11-3) struck out 11 batters and held the D-backs to two runs on seven hits over eight innings.
Justin Upton hit a two-run homer and Chris Young added a solo shot for Arizona.