Cueto (9-5) held the Nationals scoreless until Ryan Zimmerman homered on his first pitch of the ninth inning. Cueto allowed six hits, struck out five and did not walk a batter.
Francisco Cordero came on to get the final three outs for his 24th save in 29 chances, although he needed a game-ending double play to get out of a bases loaded jam.
Ramon Hernandez drove in a run for the Reds on a groundout.
Ross Detwiler (1-3) pitched six innings, his longest outing of the season. He allowed one run and seven hits while striking out a career-high seven and walking two.
The only blemish for Detwiler was Votto's 20th home run with two outs in the first inning.
Cueto, who opened the game by striking out the first three batters, narrowly missed his second shutout of the season. He leads the majors with a 1.89 ERA after the outing gave him enough innings to officially qualify.
Washington had runners reach third base in the second and fourth innings, but each time Cueto easily got out of the jam.
Cincinnati posed a scoring threat in the third when the Reds loaded the bases with one out. Brandon Phillips singled, Dave Sappelt doubled and Votto walked before Detwiler struck out Jay Bruce and Miguel Cairo hit a fly ball to shallow right field to end the inning.
The Reds picked up an insurance run in the eighth. They had a chance to pick up a few more but left the bases loaded.
Consecutive singles by Votto and Bruce against reliever Sean Burnett put runners on the corners with no outs. Cairo grounded sharply up the middle, and Burnett snagged it and threw to third to catch Votto, who had started for home on the play. Another walk by Burnett loaded the bases.
Ryan Mattheus replaced Burnett, and Hernandez hit a grounder up the middle that was fielded by shortstop Ian Desmond. A slight slip when Desmond fielded the ball left him unable to turn a double play, but he did throw out Hernandez while Bruce scored.
Another walk by Mattheus loaded the bases for Cueto, who grounded to second to end the inning.
Cordero entered after Zimmerman's homer. After a groundout, Jayson Werth walked, Danny Espinosa singled and Jonny Gomes reached on shortstop Paul Janish's error to load the bases. Wilson Ramos then grounded into a double play.
NOTES: Nationals RHP Steven Strasburg, who had Tommy John surgery last year, made his third minor-league rehab start for Class A Hagerstown. Nationals manager Davey Johnson said Strasburg may eventually replace RHP Jordan Zimmermann, who has an innings cap this season because of his 2009 Tommy John surgery. Johnson said Zimmermann likely has three more starts, and the manager speculated Strasburg may fill his spot on Sept. 2. ... Desmond batted leadoff for the first time since April 14. ... Phillips led off for the first time this season. ... Zimmermann (7-10) starts Thursday against Reds RHP Bronson Arroyo (7-9) in the final game of the series.