The most disheartening part for the Brewers? Even with Friday's loss, they have won 10 of their last 16 games -- yet they trail the first-place Reds by 8 1/2 games.
That matches Milwaukee's biggest division deficit this season.
"We've been playing so well, and we need these games, especially against this team," said Brewers starter Marco Estrada, the victim of all three home runs. "They're in first place, we're trying to catch up, and when you go out and make mistakes in the seventh inning, it just kills you inside. Every pitch counts right now."
The seventh inning was when Bruce and Rolen went deep, but the Reds went ahead for good back in the fourth. Estrada retired the first 10 Reds he faced before Cozart hit a Great American Ball Park special, a line drive that snuck into the front row of the left-field seats for a 1-0 lead.
That home run supplied the game's only run until the seventh, when Bruce and Rolen each worked into 2-0 counts before connecting with an Estrada fastball.
"I've got to focus a little better in the later innings," Estrada said.
Bailey's only trouble came in the first, when Carlos Gomez and Ryan Braun -- who was 2-for-4 and became the 11th player to log 1,000 hits in a Brewers uniform -- singled to give the Brewers runners at first and third with one out. Bailey struck out Aramis Ramirez and Corey Hart to escape the jam.
In the fifth, after Martin Maldonado's one-out double, Bailey struck out Cody Ransom and Estrada.
Bailey beat Milwaukee for the first time in his career by allowing only one run on six hits in eight innings, throwing first-pitch strikes to 18 of 29 batters and racking up 10 strikeouts versus no walks. He has surrendered one earned run in eight innings in consecutive starts, and is 4-0 with a 1.76 ERA over his last four outings.
It was just the sort of pitching performance the Reds will need while their star first baseman, Joey Votto, is on the disabled list. Votto will miss about a month after knee surgery.
"You're not the same without Joey, but the guys are picking up the slack," Reds manager Dusty Baker said. "Any time you get pitching like that, it makes it a lot easier for when you do hit a homer and score a run."
Hart agreed: "For them to lose Votto, they're going to need guys to step up. [Bailey] stepped up a lot."
Bailey was 0-5 with a 6.50 ERA in 10 previous starts against the Brewers. They had beaten him twice in 2012. Friday was different -- Bailey threw his fastball with less velocity, by manager Ron Roenicke's measure, but much better command, setting him up to use a strikeout-inducing slider.
"I knew that I never really did that good against them," Bailey said. "You just try to put it behind you and go from there."
Estrada, meanwhile, remained winless this season after allowing three runs on seven hits in seven innings. He struck out five, didn't walk a batter and helped wake up a couple of slumbering Reds.
Cozart was in a 1-for-21 slump before hitting his home run in the fifth inning. Bruce was 0-for-19 before his double in the fifth followed by his homer in the seventh.
Bruce, who has more home runs (21) and RBIs (46) against the Brewers than any other opponent, is 6-for-14 with five long balls against Estrada.
"He's been tough on me," Estrada said. "When I make my pitches, I get him out, and at points I feel like I'm going to make good pitches to him, and I flip one up there and he just crushes it every time."
Estrada missed low to both Bruce and Rolen on the pitches that preceded the home runs.
"I let it get to me, I guess, and I made bad pitches after that and I got hurt," he said. "The focus should always be there. There's no excuse to lose focus."
The Bruce blast loomed large when the Brewers finally got to Bailey in the top of the eighth, when Maldonado singled and scored on Norichika Aoki's double to left field. That hit cut the Brewers' deficit to 3-1.
But Reds closer Aroldis Chapman dominated the three Brewers hitters he faced in the ninth. He struck out Braun and Ramirez before Hart hit a game-ending groundout.
"I figured we would come in and score some runs," Roenicke said. "But Bailey did a nice job."