Miley (9-3) retired 20 of the first 21 batters he faced before giving up a homer to Alfonso Soriano in the seventh inning, then worked out of a jam in the eighth with runners on second and third.
Jason Kubel hit a solo homer off Garza (2-6) and Upton broke open a tight game with a two-run single through the left side off Manny Corpas in the eighth inning.
Arizona has won 10 of 11 at home and 12 of 17 overall to creep up the NL West standings.
The Cubs had four hits and were swept in a three-game series by the Diamondbacks for the first time since 2001. Chicago has lost four straight and eight of 11, dropping its record to a baseball-worst 24-48.
The Diamondbacks had been on an offensive tear, scoring 46 runs the previous five games, their most in the same span since 2000 "
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