In front of 41,750 fans, Cueto pitched seven shutout innings, allowing just three hits and striking out nine, marking his fourth straight quality start.
"That's what aces do," Reds manager Dusty Baker said. "That's what All-Stars do. That's what potential Cy Young Award winners do. They stop bad streaks and they create other good streaks. It was a great game by Johnny."
It was an extra special evening for Cincinnati, as Reds fans watched three former greats in Sean Casey, Dan Driessen and John Reilly get inducted into the Reds Hall of Fame on the field before the game.
With several other former greats in attendance, like Johnny Bench, Joe Morgan, Dave Concepcion and Cesar Geronimo, Cueto said he felt some added adrenaline.
"I got a little bit more energy today when I saw those people on the field today," Cueto said. "When I saw them, I kind of pumped it up a little bit."
Cueto is 4-0 in June with 21 strikeouts and a 1.49 ERA. In that span of four games, he has allowed just 18 hits, five runs and three walks.
The Twins only made it to second base twice.
"I think you saw the deception and the mix that [Cueto] has," Twins manager Ron Gardenhire said. "The fastball jumps pretty good, he backdoors the breaking ball pretty well and he's got a great changeup. He was tough. We never could get any big hits against him or put anything together."
The Reds' offense had registered just one hit through the first three frames, before opening up for a four-run fourth.
Brandon Phillips continued his steady production, cranking his 10th home run of the season on a two-run shot to straightaway center to put the first runs on the board.
Jay Bruce followed with a single and the hot Scott Rolen answered with a follow-up RBI double off Twins start Brian Duensing, who was making his first start of the season.
Rolen was 2-for-3 on the day and scored twice. After missing more than a month of action with a strained left shoulder, Rolen has tallied seven hits, one homer, five RBIs and a .389 batting average in five games since returning to the lineup on June 18.
"I've had a good year these last four days," Rolen said. "I've felt more comfortable swinging the bat and in a better position."
Right-handed reliever Anthony Swarzak replaced Duensing in the fourth. He recorded a quick out before walking Ryan Hanigan to bring Cueto to the plate.
With runners at the corners, Cueto helped his own cause, laying down a well-executed sacrifice bunt to score Rolen and increase the Reds' advantage to 4-0.
"It's a hard play to defend," Rolen said. "Generally, the third baseman is going to come down the line, so as a runner, you can follow him down as far as he goes. If you have your eye on the second baseman, you can kind of follow him and see how much he gives you down the line. I was able to get quite a bit and when he flipped it to first, I can go ahead in."
Cueto drove Rolen in again in the sixth inning on an RBI groundout for his second RBI in as many at-bats to tack on a fifth run.
"That was great by Johnny," Baker said. "It shows his determination. When he first got here, he couldn't spell hit and now he can hit a little bit. He works at it."
Despite Rolen's hot hand recently, Baker said he plans on resting his 37-year-old veteran in Sunday's rubber match.
"We're going to find a way to play everybody," Baker said. "That's how I do, and that's how you stay strong for the whole year and that's how you keep guys healthy. It's a big game tomorrow and we want to win the series."