Zack Cozart singled against Ronald Belisario (5-7) with one out and the score tied 2-2 in the ninth and Hanigan followed by lacing a hit into the left-field corner, sending Cozart all the way around for the game-winning score.
Jay Bruce belted two solo homers -- his 28th and 29th of the season -- as the Reds took a third straight from the National League West-leading Dodgers and a fourth consecutive win overall.
Aroldis Chapman (4-5) earned the decision for Cincinnati, which pulled into a second-place tie with Pittsburgh 1 1/2 games behind NL Central-leading St. Louis.
Reds starter Homer Bailey struck out nine over seven innings, allowing a pair of runs on six hits.
Hanley Ramirez belted a solo homer and added an RBI double for the Dodgers, who dropped a fourth straight.