Cueto allowed two earned runs on four hits in seven innings, and Adam Dunn and Jay Bruce each homered, helping the Reds complete a three-game sweep of the Braves with a 6-2 victory before 35,942 fans at Great American Ball Park.
Total attendance for the three-game weekend series was 111,542, with those fans witnessing the Reds' first sweep of the Braves since Sept. 1996.
The Reds went 5-1 on the homestand. They have won seven of their past nine games.
"Hopefully, we can find a way to bring what we've had at home on the road," said Dunn. "The crowd got our blood flowing the past couple days. They were into every pitch."
Ken Griffey Jr. did not hit career home run No. 600 on Sunday afternoon, but he didn't entirely disappoint the fans, going 2-for-3 with a double and a run scored.
"My biggest thing is getting a win," Griffey said. "You guys talk about it more than I do. I'm not worried about it. If I hit the ball hard enough, it'll go. I'm concentrating on doing the small things -- getting base hits, getting guys over. If something bigger happens, we'll talk about it."
The crowd stood for each of Griffey's at-bats in anticipation of the historic homer and booed vociferously when he was intentionally walked in the seventh.
"[Braves manager Bobby Cox] is managing to win," said Reds manager Dusty Baker. "He's managing to keep the game close. He's not managing for our fans or anybody else. He did what he's supposed to do. I saw that a lot with Barry Bonds."
Cueto walked just one batter and struck out three in a 100-pitch effort.
"The key for him is commanding his fastball," said Reds catcher Paul Bako. "That's the key for him. We'd like for him to be a little more consistent. Everything else will take care of itself. He dominated a good lineup today. He showed what he could do when he's on."
There were only a handful of hard-hit balls off Cueto in the first six innings -- Jerry Hairston Jr. made a leaping catch of pitcher Tim Hudson's line drive to end the third and Gregor Blanco's fly ball sent Dunn back to the warning track earlier that inning.
Cueto retired the first 14 batters he faced Sunday before walking Jeff Francoeur with two outs in the fifth.
The Braves' first hit came on Blanco's bunt single leading off the sixth. A charging Edwin Encarnacion fielded the bunt, but Blanco reached first just ahead of the throw.
The crowd reacted negatively when the scoreboard revealed Blanco was credited with a base hit.
Dunn hit his 15th home run of the season on the first pitch from Hudson in the second. The homer traveled an estimated 420 feet to right field and put the Reds ahead, 1-0.
"I was just looking for something early to swing at," said Dunn. "He gave me something up."
Bruce, who won Saturday's game with a walk-off homer in the 10th, hit his second career home run on a 3-2 pitch from Hudson in the third to make the score 2-0.Bruce finished off a magical week by going 2-for-3 with a homer and two RBIs.
Later in the third, Phillips doubled over Blanco's head in center, scoring Griffey to put the Reds up, 3-0. Phillips was thrown out attempting to reach third on the play.
Cueto ran out of steam in the seventh. With one out, Mark Teixeira's solo home run sailed just inside the right-field foul pole to make the score 3-1. Brian McCann followed with his 10th home run of the season to bring the Braves to within a run. It was Atlanta's third set of back-to-back homers this season, and McCann has been a part of each set.
Jeff Francouer followed the homers with a double, but Cueto retired the last two batters in the seventh to strand the potential tying run at second base.
"He was coming in on those guys the whole game," said Baker. "If you're getting them out, why change? He only made a couple bad pitches. He's got that extra gear. He needed it to get out of trouble."
Hudson pitched six-plus innings, allowing four runs on seven hits before leaving the game in the seventh with a strained left hamstring. He'll be reevaluated Monday.
The Reds sealed the victory with a three-run seventh. Hairston's perfectly-placed squeeze bunt scored Encarnacion. An RBI hit by Bruce gave the Reds a 5-2 lead. Bruce later scored on Buddy Carlyle's wild pitch to make the score 6-2.
Jared Burton pitched two scoreless innings in relief.
"I'm looking forward to my first road trip," said Bruce. "We're going on the road on a roll. We just need to keep the momentum going. It's been a crazy week. I'm just excited to help this team win."
Jeff Wallner is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.