The outcome prevented the Reds from clinching the National League Central title after they had wrapped up no worse than a tie when the St. Louis Cardinals lost during the afternoon to the Chicago Cubs.
Cincinnati, already ensured at least a wild card berth, owns an 11-game lead over St. Louis with 11 games to play.
Los Angeles closed within two games of St. Louis in the crowded chase for the second NL wild card berth.
The Reds and Dodgers had been tied since the fourth inning when Sam LeCure (3-3) came on to work the 10th.
He promptly hit Elian Herrera to open the inning and Herrera moved to second when A.J. Ellis was safe on a fielder's choice grounder.
Ronald Belisario (8-1) struck out five of the six batters he faced during the eighth and ninth innings to get the win. Brandon League worked the bottom of the 10th for his 13th save.