Cueto (6-8) pitched 6 1/3 scoreless innings, with four of the five hits he allowed being singles. He walked three, hit two batters and struck out two.
"He threw a great game," Reds manager Dusty Baker said. "He had outstanding tempo going. He controlled both sides of the plate."
Although he had only one 1-2-3 inning the whole night, Cueto escaped jams and picked up two double plays on the ground. His toughest situation came in the Cleveland second inning when runners were on second and third with one out after catcher Paul Bako's passed ball.
With two outs in the third, Cueto loaded the bases when he drilled Franklin Gutierrez in the ribs with a fastball. The inning ended when Sal Fasano struck out on a slider in the dirt.
"That was huge," Baker said. "He got out of that jam. Invariably, with most good pitchers, if you don't get to them early, you don't get to them. Johnny got out of that jam -- and that was big."
In the fourth, Cueto also escaped cleanly after having runners on first and second and one out.
Unlike each of his last two starts where he received one run of support, on Saturday, Cueto was given an early lead to work with. In the top of the first, second batter Adam Dunn jumped on a 1-0 Paul Byrd pitch for a solo home run to right field and a 1-0 Reds lead.
In the third inning against Byrd (3-9), Bako snapped a 0-for-14 skid with a two-out, bases-loaded double to the left-field corner for three RBIs. It was a nice turnaround for the Reds, who had lifeless bats during a 6-0 shutout loss to the Tribe and C.C. Sabathia on Friday.
With a 4-1 record in Interleague Play against Cleveland this season, Cincinnati has claimed the Ohio Cup series.
"That's what we've been missing. That was huge," Baker said of the Bako hit. "We went from [being up] 1-0 to 4-0. Johnny seemed to really settle down after that. He wanted it big time."
A three-start losing streak for Cueto is over. It had started on June 11 with an eight-walk outing during a 10-0 loss to the Cardinals, but he's been nothing short of solid since. His best outing of the season came last Sunday vs. the Yankees, but it was cut short with one run allowed and seven strikeouts after five innings because of a rain delay.
Over his last three starts, Cueto has a 1.47 ERA. After 17 starts overall, he has a 4.68 ERA with 37 walks and 83 strikeouts in 57 innings pitched.
"I've been working on my slider and changeup," Cueto said through interpreter Edinson Volquez. "Those two pitches have been working for me the last two games. My fastball is good right now."
What's been remarkable is that Cueto's last two outings have come on the road, where he hasn't been good this season. Entering the night, he was 1-6 with a 6.49 ERA in the road grays compared to 4-3 with a 4.11 ERA at Great American Ball Park.
"Hopefully, he can get on a roll in the second half and get him and ourselves back to .500," Baker said. "Then everybody feels better."