Rodriguez drew a one-out walk off reliever Jeremy Hall, advanced to second on Jose Tabata's groundout. Pedro Ciriaco hit a sharp roller to third base, and Manuel Mayora's throw to first was wild allowing Rodriguez to score.
Rays catcher John Jaso tied it 4-all in the top of the ninth with a one-out, solo homer off Chris Leroux.
Paul Maholm yielded three runs and five hits in five innings. The left-hander walked one and struck out five.
David Price pitched four innings and gave up one run on five hits. He walked one and struck out three.