Heyward's sixth-inning rocket off of Teixeira's left heel -- which Teixeira said might have been the hardest-hit ball he's ever had hit to him -- accounted for the go-ahead knock, nudging the Braves ahead as New York suffered its first loss since June 7.
The ball painfully struck Teixeira and ricocheted to the center of the diamond as Brian McCann trotted home safely, an unwelcome sight for Yankees starter Hiroki Kuroda, who permitted four runs as he gritted through seven tough innings.
"This is a tough loss," Yankees manager Joe Girardi said. "We had some opportunities and we just weren't able to come through. We've been playing well and we still played a pretty decent game tonight."
The Yankees finished 2-for-11 with runners in scoring position and saw both Teixeira and Curtis Granderson thrown out trying to score, though Girardi said he had no issue with the aggressive plays.
Teixeira was cut down by a healthy margin on Nick Swisher's fifth-inning single to right field off Braves starter Tim Hudson, as Heyward played shallow and uncorked a seed that arrived in plenty of time.
"I knew Swish hit it hard and I know Heyward's got a really good arm, one of the best outfield arms in baseball," Teixeira said. "We were just hoping in that situation that he made a poor throw, and he didn't. He made a great throw."
Granderson was tagged out at the plate trying to score in the seventh on a fielder's-choice grounder to third baseman Chipper Jones. The Yankees managed one hit in the last four innings against four Atlanta relievers, including Craig Kimbrel, who pitched the ninth for his 20th save.
"Winning takes care of a lot of things," said Russell Martin, who busted his bat grounding into a double play to end the eighth inning. "I'm not really concerned. Odds are, it's probably going to turn around at some point."
The Yankees were able to manage three runs -- two earned -- in five innings against Hudson, who walked five and struck out five.
"Hudson is tough. If you get a couple off him, that's a good night," Martin said. "He's a ground-ball pitcher, so you're going to hit ground balls. You just hope a couple ground balls get through. Today, we just couldn't really get to him."
The 10-game winning streak marked the longest in the Majors this season, as well as the 29th instance of a double-digit winning streak in franchise history. They fell one victory shy of tying their longest run of the last 50 years, having last compiled an 11-game winning streak from Aug. 31-Sept. 10, 1985.
"You don't look too deep into it," Teixeira said. "We've been playing really good baseball lately, so we're not going to fret too much over one game."
Kuroda accepted his share of the blame, as the four runs marked his most over his last six starts, though credit deserved to be given to the Braves for making the right-hander work hard.
"I really didn't want to give up that last run," Kuroda said through an interpreter. "If I kept it within three runs, I knew the offense was going to do its job. I really regret giving up that run."
Heyward tripled and scored on a third-inning groundout, while Jones and Andrelton Simmons contributed run-scoring hits in Kuroda's tough 32-pitch fourth inning.
"I think I was trying to be too perfect with all my pitches, and I was really being aggressive in the first three innings," Kuroda said. "In that [fourth] inning, I wasn't being aggressive."
Returning to the lineup after missing two games with a bruised left thigh, Swisher slugged a two-run double in the second inning, and a pair of fourth-inning errors led to the Yankees' third run.
Raul Ibanez's bad-hop grounder ate up first baseman Freddie Freeman, and after a walk, Martin blasted a shot down the third-base line that was scored an error on Jones, moving Ibanez home safely.
"We just kind of ran out of innings pretty much," Swisher said. "We feel like we're playing good ball right now. I guess you could say it's a little easier to shrug this one off, but no one likes losing."