"He wasn't as sharp as we've seen him before, but we did a nice job handling him," said Braves Manager Fredi Gonzalez. "The first two guys get on base six times on hits, that kind of set the tone. I felt we had some pretty good at-bats up and down the lineup.
"He came out throwing a lot more offspeed than normal tonight early in the game, and we were laying off it and putting good swings on the ones he made mistakes on," added catcher Brian McCann.
McCann snapped a 32-at-bat homerless streak and Tim Hudson threw six shutout innings before relenting.
The win gave the Braves a split of the two-game mini-series and raised their record to 9-6 at Turner Field. The Reds saw their road record even off at 9-9 and missed an opportunity to match their season-high three-game winning streak.
Bourn and Martin Prado each had three hits, and McCann had two for the Braves, who pounded out 12 hits while playing without first baseman Freddie Freeman.
McCann, who had his second multihit game in the last three, got the Braves on the board in the second inning, taking a 2-1 pitch out to right field off Cueto (4-1). The blast was the sixth of the year for the Braves catcher, but his first in nine games, going back to his grand slam in the fifth inning off Roy Halladay in Atlanta's 15-13, 13-inning win over Philadelphia on May 2 at Turner Field.
McCann's at-bats typified the Braves' attack all night.
"Our guys are putting together some really good at bats," said Hudson. "We're making it tough on the pitcher. Cueto's been throwing the ball really well. I think it was the combination of, he came across a lineup that'll battle you and he might not have had his best stuff tonight. It was just one of those things that we were able to take advantage of.
"In years past, we may not have been able to take advantage of it, he might have been able to get into a groove. We got some timely hits and got some crooked numbers up there."
While Bourn has been superb as a catalyst -- he has now reached base in 30 of the team's 37 games and is hitting .461 over his current five-game hitting streak -- the rally that doomed Cueto was started by Jack Wilson.
"Jack's a defensive specialist, but if you look at the back of his baseball card, he's a guy that had 200 hits one year," said Gonzalez. "He's not an automatic out. You have to respect him."
He earned some respect in the third, leading off with a single that started Atlanta on a four-run, five-hit binge during which it sent 10 men to the plate. Prado and Chipper Jones, back in his customary three-spot with Freeman getting the night off, had RBI singles, and Jason Heyward added an RBI double.
"We had good hitting that inning," said Bourn, who singled in the inning and raised his career average against Cueto to .375 (9-for-24), with his 2-for-3 night against him. "When we put a good inning together, we can score some runs. Throughout our lineup, it's tough to get through all of us. We just try to make it hard on the pitcher. We know he's thinking up there. He has a lot on his mind if we can grind him."
Cueto, who entered the game as the National League ERA leader, with a 1.12 mark, left Atlanta with a 1.89 ERA, in sixth place. Atlanta's Brandon Beachy, who starts Thursday against the Florida Marlins, now leads the NL in ERA, at 1.60.
The win marked the second time in three games that the Braves KO'ed one of the NL's ERA leaders, having gotten to St. Louis' Lance Lynn on Sunday.
"I think it all starts with Michael Bourn," said McCann. "He's as good as they come. He impacts every single game, his speed's off the charts, and when he gets on base he wreaks havoc on the pitcher."
The Braves peppered Cueto for six runs (five earned) and eight hits, both season highs. The run total equaled Cueto's total for the entire month of April. He lasted four innings, throwing 82 pitches, 50 for strikes.
Hudson (2-1) went seven innings for the second straight start, throwing a season-high 98 pitches (58 for strikes). He shut out the Reds over six, limiting them to five hits, and he didn't allow a runner to reach third base. The Reds finally reached him for two runs and four hits in the seventh.
"I think Huddy set the tone, really, to keep us in the ballgame," said Gonzalez. "Six scoreless innings. He gave up two there in the seventh."
It marked back-to-back quality starts for Hudson, who handcuffed the Cubs in his last outing. Most important, he's feeling good following his starts.
"I'm feeling better each time out," said Hudson, who raised his record to 4-1 with a 3.10 ERA in seven career starts against Cincinnati. "Each week that passes by I get a little more healthy. I'm not really concerned with it. I feel like I'm feeling better than I have in a really long time from a health standpoint."
Relievers Kris Medlen and Craig Kimbrel finished off the Reds. Kimbrel needed 26 pitches to retire the side, but Gonzalez was glad he got his closer some work.
"It's twice in seven days if we don't use him today," he said. "We need to use those guys.