Heyward's two-out opposite-field single capped a three-run eighth inning, and the Braves upended the Mets, 8-7, on Saturday at Turner Field.
The win was only the third for the Braves in 36 games when they trailed after seven, but it was big.
"These guys have a little swagger right now," said third baseman Chipper Jones. "We're playing well, we've got a little winning streak going here. The guys are fighting and scratching and clawing to keep it going."
The Braves entered the eighth trailing, 7-5, but put together an inning that was a microcosm of the game itself.
Brian McCann, down 1-2, worked a walk against Tim Byrdak. Dan Uggla then singled off Pedro Beato to put runners on first and second.
But just when things looked to be going the Braves' way, the Mets made big pitches. Tyler Pastornicky, recalled from Triple-A Gwinnett on Saturday morning, was unable to move up the runners, bunting a third strike foul. Then closer Bobby Parnell was summoned, and he struck out pinch-hitter Juan Francisco.
Some of the air was out of the Braves' balloon, but not all of it. Michael Bourn sent a 3-1, 97-mph fastball back up the middle for an RBI single that cut the deficit to one run.
"I just try to tell myself, 'Don't try to do too much with it. Relax up there and hit the baseball,'" said Bourn. "It didn't just start with me, [Martin Prado] or J-Hey. It started when [McCann] walked, and Dan putting good at-bats together, and then we just kept going from there. We didn't give up on it, and we did it with two outs, too."
Batting after Bourn, Prado, down 1-2, went the opposite way, ripping a 99-mph pitch between first and second to tie the score.
Up stepped Heyward, who worked a favorable count, then sent a 2-0 pitch to left, scoring Bourn with the go-ahead run.
Craig Kimbrel did the rest, striking out the side in the ninth to earn his 27th save and assure the Braves their sixth straight win.
Anthony Varvaro (1-0) got the win, with Parnell (2-2) taking the loss.
"What a game to win," said manager Fredi Gonzalez. "A lot of positive stuff in today's game. Hopefully we can keep it rolling."
Freddie Freeman, who went into the game with a five-game hitting streak, continued his torrid hitting, going 3-for-4. He was involved in the first two scoring rallies, starting the three-run second with an infield hit, and capping the fifth with a booming two-run double to right-center, both hits coming off Mets starter R.A. Dickey.
"I think the top of the order -- Bournie, Prado, Jason, Chipper, Freeman and Mac -- is starting to come to life," said Gonzalez. "That's a pretty good top six guys here. We get those guys firing on all cylinders, and it's a pretty long lineup you have to try to get through."
Freeman's two-run double gave the Braves a two-run lead and followed a reversed call by the umpires on a Heyward looper to shallow left. Mets left fielder Jordany Valdespin made a sliding attempt but short-hopped the ball. Third-base umpire Dale Scott originally called Heyward out, as well as Prado, who was doubled off first. But Scott, the crew chief, asked for help, and the call was reversed. Prado was awarded second and Heyward first.
Mets manager Terry Collins came out to argue and was ejected. One out later, Freeman gave the Braves the lead.
Gonzalez was pleased with the way the umpires handled the play.
"They got it right," he said. "At the end of the day, it's [their job to] get the play right, and they did."
But the Braves, who led, 3-1, after two innings courtesy of Eric Hinske's two-run double and Bourn's RBI single, could not hold the lead.
Neither Braves starter Tommy Hanson nor Dickey were part of the decision, with Hanson lasting 5 1/3 innings, allowing six runs, all earned, on nine hits, while Dickey went five innings, allowing five earned runs on eight hits. It was the third time in four starts that Dickey has allowed five earned runs.
Hanson had been the pitcher of record on the losing side and Dickey the pitcher on the winning side until the eighth-inning rally.
"I just felt like I could never really get in a groove," said Hanson, who with the no-decision, has lost only once in his last eight starts. "I didn't feel like I had my best stuff today, and my command was shaky. There were times that I felt good and confident, and there were other times I just wasn't throwing it where I wanted to go."
The Braves, who had eight hits off Dickey, managed only one hit off the Mets' bullpen until getting the four straight hits off Beato and then Parnell.
Prado chalked up his team-high 34th multi-hit game with the two hits, while Bourn stayed right behind him, with 33. McCann, who was back in the lineup following a one-day absence to witness the birth of his son, Colt, looped a single to shallow right in the second inning to extend his hitting streak to six games, but Jones' streak is over at 14 games.
Jones wasn't too upset about seeing his streak end.
"Hitting streaks are going to come and go," he said. "I'll take the 'W' and the [team's] six-game winning streak over a hitting streak."