The Braves increased their lead over Philadelphia in the National League East to 3 1/2 games when the Phillies had their seven-game winning streak halted by Washington.
Cincinnati tied it at 4-4 in the eighth on Joey Votto's solo homer, his 27th of the season. Atlanta then produced the winning runs against Francisco Cordero (3-4).
Melky Cabrera drew a one-out walk in the 10th and, one out later, Martin Prado walked as well. Heyward then drove a 3-2 delivery to left and, with the runners going on the pitch, Prado was able to score all the way from first.
Billy Wagner came on to protect the lead in the bottom of the 10th and he put two on with one out before getting Miguel Cairo on a fly ball to deep center and Drew Stubbs on a strikeout.
It was Wagner's 24 save and ensured the victory for Jesse Chavez (3-2), who worked the bottom of the ninth.