Joe Saunders, the listed Arizona starter, was unable to take the mound when he developed shoulder tightness while warming in the bullpen. Josh Collmenter replaced him and went four innings before giving way to a string of four more relievers who held the Cubs scoreless over the final five frames.
The win went to Brad Ziegler (4-1), the second Arizona pitcher, who gave up two hits and struck out three while working the fifth and sixth innings.
Geovany Soto gave Chicago the lead with a homer off Collmenter in the fourth, but Kubel put the Diamondbacks on top in the bottom of the inning.
Ziegler helped his own cause when he delivered a two-out single in the fifth and later scored on a base hit by Aaron Hill.
The loss went to Jeff Samardzija (5-6), who gave up five runs on seven hits in five innings.