The National League Central-leading Cubs won earlier in the day, so the Brewers fell to 2 1/2 games back with eight games to play.
"We're 2 1/2 good days away from being back in first place," Brewers manager Ned Yost said. "As far as I know, we've got a week left."
Hardy was more blunt about the Brewers' chances of getting to the postseason for the first time in 25 years.
"I guess we have our work cut out for us, that's for sure," Hardy said. "We just have to go out there and win ballgames. We can't worry about the Cubs, because they're going to do what they're going to do. We have to root for them to lose, too.
"We definitely would rather be in their seat."
Hardy's 26th home run broke up a no-hit bid by Atlanta starter John Smoltz and tied the game at 2, and Hart's 22nd homer gave Milwaukee a 3-2 lead in the 10th. The Brewers stranded runners at second and third later in that inning but still had a chance to win when Cordero, who entered with a franchise-record 44 saves and had converted eight straight, retired the first two hitters he faced on ground balls.
Thorman ambushed a first-pitch fastball and launched a home run to right field, tying the game at 3. Entering the at-bat, Cordero had faced 256 hitters this season and surrendered one home run.
Cordero did not address reporters after the game. He said he would do so on Sunday morning.
The Brewers left the bases loaded in the top of the 11th inning against Braves reliever Joey Devine (1-0), and Atlanta won it in the bottom of the inning against Seth McClung (0-1), who walked the only batter he faced.
The Brewers brought in left-hander Brian Shouse to turn switch-hitter Chipper Jones to his weaker right side, and Jones bounced what could have been a double-play ball to second baseman Rickie Weeks, who bobbled it.
"I don't know -- I just missed the ball," said Weeks, who believed it would have been a double play.
"We just didn't make the play," Yost said. "What I think doesn't matter. Rickie played a great game. Things happen."
Teixeira, also a switch-hitter but one with a better average when hitting right-handed, singled to right field to win the game. Brewers right-hander Scott Linebrink was unavailable to pitch because of his recent workload.
The loss negated another stellar start by Brewers rookie Yovani Gallardo, who had not allowed a run in his previous 21 innings and three starts but was touched up quickly by the Braves, allowing a run in the first inning and another in the third on a Jones homer.
The 21-year-old Gallardo was otherwise tough, holding the Braves to those two runs on three hits in seven innings. In his last five starts, Gallardo has given up only four runs in 35 innings, posting a 1.03 ERA.
He had nothing to show for his effort on Saturday.
"There's nothing we can do about it now," Gallardo said.
How good was Smoltz? The Brewers were no-hit by Detroit's Justin Verlander in June, and Hardy said that Saturday had the same feel, especially after second baseman Kelly Johnson and Smoltz combined on an outstanding defensive play to retire Johnny Estrada ending the fifth inning.
"In the fifth and sixth inning, yeah," Hardy said. "After Kelly Johnson made that play in the hole, [Smoltz] got really pumped up. I was thinking to myself, 'He's thinking about a no-hitter.' It crossed my mind."
Hardy said that Smoltz established the inside corner the first time through the order. Then he threw his "invisible slider" the rest of the way, though Hardy hit one in the sixth.
"He hung three sliders all day, and they were all in that at-bat," Hardy said. "I took the first two, and then he threw another one. They were probably the only bad pitches he threw the whole game."
The Brewers had their chances late. After Hart's go-ahead homer, they had runners at first and third with veteran Craig Counsell at the plate. Facing left-hander Royce Ring with speedy pinch-runner Mel Stocker at third, Counsell, looking to stay out of a double play, elected to attempt a drag bunt even with two strikes, but he fouled it off for out No. 2. After Bill Hall took second on defensive indifference, Weeks was called out on strikes to end the inning.
"I have to get it done," Counsell said. "I thought that was the best way to get the run in. I had a chance to do it. I just didn't get it done. With Mel running so good, you get a bunt down, he's going to score. That was kind of my thinking."
Yost had no problem with Counsell's call.
"Counsell is a polished, Major League, professional player," Yost said.
In the 11th, Hardy led off with a single and moved to second when pitcher Jeff Suppan executed a sacrifice bunt in his first career pinch-hit appearance. Four batters later, catcher Damian Miller worked a 3-0 count against Devine, took a called strike and then swung on 3-1 and popped out in the infield.
"We're still in it -- we're not going anywhere," Counsell said. "It's a tough loss -- there's no hiding behind that -- but we still have eight games left, and we're [2 1/2] out. It's not a huge climb. We just have to keep plugging."