Cueto (9-3) collected his fourth win in four starts and third straight in which he has allowed one or fewer runs.
The Dominican right-hander controlled the Twins on three hits while striking out nine and issuing only one walk as the National League Central-leading Reds evened the three-game series.
Cueto also delivered two RBI. Brandon Phillips belted a two-run homer for Cincinnati, which broke a four-game losing streak.
Brian Duensing (1-3), making a spot start, surrendered four runs on four hits over three innings for Minnesota.
The Twins lost for the fourth time in seven games.
Swim Week Miami Beach 2014 [PHOTOS]