Kyle Schwarber also connected as the Cubs won for the eighth time in nine games since the All-Star break. The World Series champions improved to 51-46, just a few percentage points ahead of Milwaukee after the Brewers (53-48) lost 6-3 at Philadelphia.
Quintana (6-8) struck out seven in six innings in his first home start since he was acquired in a blockbuster trade with the White Sox on July 13. He pitched seven sparkling innings in an 8-0 victory at Baltimore in his Cubs debut last Sunday.
Coming off his first career shutout, Michael Wacha (7-4) was charged with five runs and six hits in six innings in his first loss since May 30.
Wade Davis finished for his 20th save in 20 chances.