Cueto (7-3) racked up his sixth career complete game and second straight victory for the Reds. The Dominican right-hander didn't issue a walk and struck out seven while lowering his ERA to 2.46.
Joey Votto went 2-for-4 with a two-run homer and three RBI while Wilson Valdez added three hits and drove in a run for Cincinnati, which came into the contest tied with Pittsburgh die first in the National League Central.
The Indians' Jeanmar Gomez (4-5) absorbed the loss despite yielding only one earned run on six hits in a five-inning stint.
Jason Kipnis drove in the only run for the Tribe, who dropped the first of a three-game Ohio rivalry series.