But Arizona responded in the next half-inning while facing Reds relief ace Aroldis Chapman (3-3), who didn't retire a batter.
Paul Goldschmidt singled to lead off and went to second on a wild pitch. Miguel Montero and Cody Ross then drew consecutive walks from Chapman and Kubel followed with sharp liner to center, scoring two runs for the win.
Brad Ziegler (4-1) earned the decision after recording the final three outs in the top of the ninth as the National League West-leading Diamondbacks racked up a fourth straight win.
Gerardo Parra went 2-for-4 with a two-run homer for Arizona.
Reds starter Mike Leake carried a perfect game into the sixth inning before D-backs pitcher Patrick Corbin singled. He allowed two runs on four hits over eight innings, walking one and striking out one.