Bruce led the Reds with three hits. Brandon Phillipshad a two-run double in the ninth, and Choo had two hits and scored three runs as the Reds split the four-game series.
Teheran (7-5) allowed five runs, seven hits and two walks in 5 1/3 innings.
Braves first baseman Freddie Freemanwas held out because of a jammed left thumb that will prevent him from playing in the All-Star game on Tuesday.
Atlanta catcher Brian McCannwas named to replace him on the NL All-Star team.
Control problems pushed up Cingrani's pitch count. The rookie left-hander, who threw 96 pitches, allowed two runs -- one earned -- four hits and three walks in four innings.
Cingrani gave up a run in the second but stranded three runners. Reed Johnson singled with two outs and scored on Gerald Laird's double. Cingrani loaded the bases with two walks, but ended the inning by snagging Jose Constanza's liner.
Atlanta's missed opportunity for a bigger inning set the stage for the Reds' four-run third. Cingrani led off with a bunt single, and Choo also singled before Votto's double and Brandon Phillips' groundout each drove in a run. Bruce's 19th homer pushed the lead to 4-1.
The Braves added an unearned run in the third. Simmons walked, moved to third on Chris Johnson's single and scored when Reds shortstop Zack Cozart caught a liner by Evan Gattisand then threw wildly to first base in an attempt for a double play.
Choo led off the fifth with his 13th homer.
Gattis was 0-for-4 in his return from the disabled list after playing only two games in his rehabilitation stint with Triple-A Gwinnett.
Gattis was the fill-in starter for Freeman, who jammed his thumb Saturday night.
Before Freeman's injury, the Braves planned for Gattis to remain with Gwinnett through Sunday. He had been out since June 18 because of a right oblique strain.
Constanza made a running catch of Choo's drive to left field in the first inning and made another leaping grab of a drive by Bruce in front of the wall in the ninth.
Reds closer Aroldis Chapman gave up Simmons' eighth homer in the ninth.