Albies connected for his 17th homer on the first pitch he saw against Cincinnati reliever Dylan Floro (2-2). It was the third extra-base hit of the game for Albies and his first walk-off homer.
The defeat snapped a season-long seven-game win streak for the Reds.
The winning pitcher was Luke Jackson (1-0), who worked a scoreless 11th.
Atlanta starter Mike Foltynewicz looked sharp in his first start since June 12. He spent 10 days on the disabled list after experiencing tightness in his right tricep in that game against New York.
The right-hander pitched five innings and allowed one run on one hit, a solo homer from Scott Schebler in the fifth inning. Foltynewicz walked four and struck out four. In 15 starts, he has allowed two or fewer earned runs 14 times.
Cincinnati's Tyler Mahle gave up three runs on five hits and four walks in five innings. He struck out five.
Atlanta got two runs in the first inning. Albies drove in Ender Inciarte with his 24th double and scored one out later when Kurt Suzuki hit a sacrifice fly to center field.
The Reds cut the lead to 2-1 in the fifth on Schebler's 10th homer, but the Braves got it back in the bottom of the inning when Nick Markakis grounded into a double play.
Cincinnati took a 4-3 lead in the seventh when Schebler doubled and scored on Joey Votto's infield grounder. Atlanta tied the game with a run in the bottom half when Danny Santana doubled in Freddie Freeman, who reached on a two-base error by Votto.
The game was delayed by one hour and 20 minutes because of rain.
--Field Level Media