Clinging to a 1-0 lead in the eighth, the Diamondbacks got consecutive one-out singles from Corbin, A.J. Pollock and Martin Prado off Sam LeCure, loading the bases.
J.J. Hoover took the mound and Goldschmidt greeted him by lining a low shot over the left-field fence for his third grand slam of the season.
It was his 31st homer of 2013, tying him with Pittsburgh's Pedro Alvarez for the National League lead and giving him 100 RBI, tops in the NL.
Corbin (13-3) took a shutout into the eighth inning before surrendering a pair of runs. He yielded six hits without a walk and struck out 10 in the 103-pitch complete game, his second of the year.
Reds starter Tony Cingrani (6-3) allowed one run on three hits before exiting after 3 2/3 innings with a lower back strain.
Chris Heisey smacked a two-run homer for third-place Cincinnati, which came into the contest trailing National League Central-leading Pittsburgh by 2 1/2 games.