The Braves struck for four runs in the seventh inning, three of them on Dan Uggla's 15th homer of the season, but Atlanta could manage only one hit against the three relievers the Phillies sent into the game.
Quintero delivered a two-run homer in the third and Howard hit a solo shot one inning later. The eventual winning run, however, came in the sixth on a double from Quintero.
Cliff Lee (10-2) took a shutout into the seventh inning before being rocked by Uggla's home run. Lee allowed eight hits without a walk and four strikeouts.
J.C. Ramirez, Antonio Bastardo and Jonathan Papelbon protected the lead. Papelbon gave up a one-out single in the ninth before completing his 18th save.
Paul Maholm (9-7) was tagged with the loss, giving up five runs on nine hits in six innings.