Trailing 2-1 with two out in the eighth, Norichika Aoki singled off Jonathan Broxton (1-1), went to third on catcher Dioner Navarro's throwing error and came home with the tying run on a Gomez single to center field.
The Brewers outfielder then stole second and scored the decisive run when the next batter, Braun, looped a 1-0 pitch that bounced in front of diving left fielder Chris Heisey for a double.
Gomez also provided a solo homer for Milwaukee, which became the first National League team to sweep the NL Central-leading Reds this season.
John Axford (4-6) earned the victory with a scoreless eighth inning and rookie Jim Henderson picked up his second career save for the Brewers.
Cincinnati starter Mat Latos hurled seven innings of one-run ball, walking one and striking out eight.
Navarro supplied the Reds' offense with a third-inning, two-run homer.
Notable deaths of 2014 [PHOTOS]
LeBron James reveals his new Nike shoes