Upton led off the inning with a single off Donovan Hand (0-5) and one out later went to second when second baseman Scooter Gennett misplayed an Evan Gattis grounder.
After Brian McCann popped out, Simmons singled to right, driving in the game-ending run.
Craig Kimbrel (4-3) was credited with the victory after striking out the side in the top of the ninth for the National League East champion Braves, who evened their three-game series.
Gattis and Freddie Freeman each went 2-for-4 with an RBI for Atlanta.
Jeff Bianchi homered and Jonathan Lucroy drove in a run for Milwaukee.