Prado doubled home Jason Kubel in the seventh inning off Tommy Layne (0-1) to put Arizona ahead 6-4, providing the eventual game-winning run.
Eric Chavez smacked a two-run homer for the D-backs, who maintained a half-game lead atop the National League West with a win in the rubber match of a three-game series.
Corbin stretched his unbeaten streak to 10 starts and provided a run-scoring single. The left-hander allowed four runs (three earned) on seven hits over six innings while walking two and fanning five.
Carlos Quentin went 2-for-4 with with a two-run homer and Kyle Blanks added two RBI for the Padres.