Philadelphia remained a half game ahead of New York in the NL East after the Mets beat the Nationals.
Happ (1-0) allowed three hits, walked one and struck out two in his fourth career start and first since getting no decision July 9 in Philadelphia's 4-2 win over St. Louis.
Chad Durbin pitched the next 1 2-3 innings before a walk to Chipper Jones gave the Braves two baserunners in eighth. J.C. Romero needed just two pitches, however, to retire Brian McCann on an infield pop up.
Clay Condrey gave up pinch-hitter Greg Norton's RBI single in the ninth, ruining a chance for the Phillies' pitching staff to earn its 12th shutout and tie Houston for the NL lead.
The Braves, who have lost two straight and 23 of 35, didn't get a runner in scoring position until Casey Kotchman's leadoff double in the fifth.
Happ was recalled from Triple-A Lehigh Valley for the third time this season on Sept. 1. He is 1-0 with a 2.11 ERA in three starts, far better than his work in three relief appearances, a span of 6 1-3 innings in which he has no record and 9.95 ERA.
The Phillies won their eighth straight at Turner Field to become the first visiting team with that many consecutive victories in Atlanta since Cincinnati had a seven-game streak in 1980.
They took a 4-0 lead in the first off Jair Jurrjens, using the rookie's early control problems and his season-long difficulty in holding runners.
After Howard's RBI single made it 1-0, the Phillies led 2-0 when Jayson Werth stole third and scored when catcher Brian McCann threw the ball into left field.
Carlos Ruiz's two-run single ended Jurrjens' 43-pitch innning. Jurrjens (13-10) gave up four runs, five hits and five walks in five innings.
Pedro Feliz's RBI groundout off reliever Blaine Boyer in the eighth made it 5-0. Pinch-hitter Matt Stairs ended the scoring with his 12th homer, a solo shot off Blaine Boyer in the ninth.
Notes: Jones is hitting .365 after going 1-for-3 with a walk to increase his lead over St. Louis' Albert Pujols by 11 points for the majors' best batting average. Pujols went 0-for-4 at Cincinnati. ... Jones has reached base safely in 40 straight games.
... With a single off Durbin in the eighth, Atlanta 2B Kelly Johnson has hit safely in 15 straight games. ... Braves LHP Tom Glavine plans to begin exercises that use a baseball as a weight on Thursday, exactly four months since he underwent season-ending elbow surgery. ... Philadelphia improved to 12-2 against the Braves this year, tying the 1956 and '65 Phillies for the club's single-season victories over Atlanta.