Right-hander Tommy Hanson allowed one run on five hits over five-plus innings to pick up his first win in three starts. Relievers Chad Durbin, Eric O'Flaherty, Cristhian Martinez and Jonny Venters finished off the Cardinals.
The Braves completed the 10-day road trip with a 7-2 record, including a sweep in Colorado.
Heyward was able to bounce back after his most futile game of the season.
"That's baseball, you've just got to forget about things, move on and stay ready," Heyward said. "You go up with the approach that you are going to get it done every at-bat. Sometimes they're going to make good pitches and sometimes you're going to be ready and you come out on top."
Heyward sure came out on top in his one-on-one battle with St. Louis starter Lance Lynn, who fell to 6-1. Heyward fouled off three successive pitches before ripping the 10th offering off the right field wall on one hop.
"It was a battle," Heyward said. "I just tried to keep perfecting my timing every pitch and hopefully I would get a pitch to hit. I know it took a lot out of him."
Heyward ripped a two-run homer in the 12th inning on Friday to lead his team to a 9-7 win in the opener. Twenty-four hours later, he put the ball in play only once during an 0-for-5 effort.
The good Heyward reappeared on Sunday, just in time to help the Braves to their 22nd win in the last 31 games.
Atlanta swept St. Louis for the first time since Sept. 11-13, 2009. After that series, the Braves lost their next seven games in St. Louis before snapping the string Friday.
"We did a lot of good stuff this series," manager Fredi Gonzalez said. "We pitched well, we swung the bats well, had some timely hitting."
Heyward broke open a scoreless game with his two-out hit in the third. Martin Prado, Freddie Freeman and Dan Uggla scored on the double. Prado began the rally with a two-out single. Freeman and Uggla drew walks to set the stage for Heyward's heroics.
"One pitch cost you the day," Lynn said. "Looking back on it now, you'd probably throw him something different."
Heyward was 3-for-15 in the series, but two of the hits were game winners.
"A lot of timely hit this whole series," Gonzalez said.
Atlanta fouled off a whopping 35 pitches on Sunday. Heyward had six fouls in his pivotal trip to the plate.
All seven of the Braves' runs on Sunday came with two out.
Hanson (4-3), who struck out nine and walked three, allowed just two hits -- a pair of singles by Rafael Furcal -- over the first five innings before tiring in the sixth. He gave up a leadoff home run to Carlos Beltran, followed by singles by Allen Craig and Lance Berkman. Durbin recorded an out and O'Flaherty struck out pinch-hitter Tyler Greene with the bases loaded to end the threat.
Hanson walked the first two batters of the game but responded with five successive strikeouts. Furcal and Jon Jay earned free passes to begin the contest. They each swiped bases to move into scoring position with no one out. Hanson got Beltran and Craig looking before dispatching Berkman.
"I felt good with all my pitches," Hanson said. "For the most part, I did a good job of locating."
The Braves put the game away with three runs in the seventh to go up, 6-1. Prado, who had two hits, drove in Tyler Pastornicky with a single. Freeman and Uggla followed with back-to-back run-producing doubles.
Heyward, Prado and Michael Bourn each used pink bats in the contest in honor of Mother's Day and major league baseball's Breast Cancer Awareness program. Freeman, who lost his mother to cancer 12 years ago, wore pink shoes as a tribute.
Bourn had two hits and added a run-scoring single in the eighth to make it 7-1. Bourn and Furcal, who had three hits Sunday, are tied for the NL lead with 51 hits. Bourn was 8-for-17 in the series.
Chipper Jones, honored before the game for his last regular-season appearance in St. Louis, entered the contest in the top of the sixth as part of a double-switch. He struck out and walked in two plate appearances.
St. Louis climbed to within 7-4 on a three-run homer in the ninth. Venters replaced Martinez and struck out Berkman to end the game.