Cueto (9-3) allowed just three hits with a walk and a hit batter. He threw 75 of his 118 pitches for strikes and fanned nine to earn the win. He also chipped in offensively with a pair of RBI. Jose Arredondo and Alfredo Simon closed out the victory in relief.
Brandon Phillips clubbed a two-run homer and Scott Rolen added an RBI double for the Reds, who snapped a four-game skid.
"He pitched the way he has been pitching because we really needed that win," Phillips said. "We've been struggling a little bit and not getting key hits. Good teams go through funks. I'm just glad we ended it and hopefully we can get another win tomorrow."
Brian Duensing (1-3) got the start for Minnesota, but lasted just three innings as he allowed four runs on four hits with two walks. Joe Mauer, Josh Willingham and Ryan Doumit each had a hit in defeat for the Twins, who have alternated wins and losses over their last seven contests.
Cincinnati broke a scoreless deadlock with four runs in the fourth. Joey Votto coaxed a leadoff walk from Duensing and Phillips followed by drilling a fastball to straightaway center field and onto the grass beyond the wall for the 2-0 advantage. Jay Bruce followed the long ball with a base hit and came around to score on a double by Rolen to widen the gap to 3-0.
Duensing was pulled in favor of Anthony Swarzak, who intentionally walked Ryan Hanigan after getting Todd Frazier to pop out to put runners on the corners. Cueto then helped his own cause by putting down a perfect squeeze bunt, which allowed Rolen to score.
Rolen roped a one-out base hit in the Cincinnati sixth. Frazier followed with a double and Ryan Hanigan was intentionally walked to load the bases. Cueto got the job done again with an RBI groundout to extend the Reds' lead to 5-0.
Bruce led off the Reds' eighth with a double and came around to score on an error by Twins third baseman Trevor Plouffe to account for the final margin.
"He was tough," Twins manager Ron Gardenhire said of Cueto. "We made him work early, made him throw some pitches. But as things went along, we never could come up with any big hits or put anything together."
Prior to Saturday's game, the Reds inducted reserve infielder Dan Driessen and former All-Star first baseman Sean Casey into the their Hall of Fame...With Phillips' fourth inning homer, there has been at least one long ball hit in each of the last 61 games played at Great American Ball Park...Minnesota fell to 15-20 on the road and 8-9 in interleague play this season...Cueto's last two-RBI game was July 19, 2010 against the Washington Nationals.