Garza (9-10) stretched his personal unbeaten streak to five starts, issuing only one walk and striking out 10 batters in a dominating performance that saw him toss 88 of his 123 pitches for strikes.
Marlon Byrd clubbed a three-run homer and Geovany Soto went 3-for-4 with an RBI double for the Cubs, who delayed the Brewers' clinching of the National League Central by taking the rubber match of a three-game set at Wrigley Field.
Milwaukee's Randy Wolf (13-10) was roughed up for six runs on 10 hits over six innings, losing for only the second time since July 23.
The Brewers' magic number to claim the division title remained at three.
Notable deaths of 2014 [PHOTOS]