Reds starter Bronson Arroyo carried a no-hitter and a 3-0 lead into the eighth inning, setting down 20 straight Milwaukee hitters until George Kottaras walked, Taylor Green doubled and pinch-hitter Corey Hart bashed a two-run double.
Norichika Aoki then chased Arroyo with a game-tying, two-out single.
Stubbs blasted the first pitch he saw from John Axford (1-5) in the next half-inning over the center field wall for the decisive blow.
Sean Marshall (2-3) earned the victory, recording the final out in the top of the eighth and Aroldis Chapman collected his ninth save for National League Central-leading Reds, who clinched their three-game series with the Brewers.
Jay Bruce smacked a three-run homer for the Reds.