Rodriguez drove in Will Venable, who had singled and moved to third on a single by Brian Giles. Rodriguez also drove in the Padres' other run, scoring pitcher Jake Peavy with a double in the fifth inning.
Peavy struck out 13 batters over eight scoreless innings, scattering five hits, but ended up with a no-decision.
Reliever Trevor Hoffman (3-6) was the winner in the Padres' fifth victory in six games.
Chris Iannetta singled in the Rockies' run.
Taylor Buchholz (6-4), victim of the Padres' winning rally, took the loss.