The Braves took a .227 team batting average into the game after being shut out 2-0 by Roy Halladay on Wednesday night. They had nine hits, including only four against the 47-year-old Moyer (2-1), who struck out four and walked two.
Philadelphia's starting pitchers allowed no earned runs as the Phillies won two of three from the Braves.
Juan Castro had three hits and Shane Victorino drove in two runs for Philadelphia.
Derek Lowe (3-1) gave up six hits and five runs, four earned, in five innings.
Moyer made his major league debut on June 16, 1986, more than three years before Atlanta's 20-year-old rookie right fielder, Jason Heyward, was born. Heyward, who was hit by a pitch from Moyer in the second inning, was 0 for 3.
Chad Durbin, who gave up one run, Danys Baez and David Herndon each pitched one inning in relief of Moyer.
Three straight singles by Greg Dobbs, Chase Utley and Ryan Howard, followed by Jayson Werth's sacrifice fly, gave Philadelphia a 2-0 lead in the first inning.
The Phillies added three runs in the third. With one out and the bases loaded, Raul Ibanez hit a possible double-play ball to Martin Prado at second base, but Prado threw high to shortstop Yunel Escobar at second base for an error as two runs scored. Castro added a run-scoring single.
Two errors by Utley helped the Braves score two unearned runs off Moyer in the fifth. After Moyer walked Melky Cabrera and pinch-hitter Omar Infante with one out, Matt Diaz hit a grounder to Castro at shortstop, setting up a possible double play. Utley missed Castro's throw to second, allowing Cabrera to score.
Prado followed with another grounder to Castro, who threw to Utley to force out Diaz at second. Utley made a wild throw to first for his second error, allowing Infante to score.
The Phillies added to their lead on Victorino's sacrifice fly in the sixth and RBI singles by pinch-hitter Ross Gload and Victorino in the seventh.
Nate McLouth doubled and scored on Brian McCann's sacrifice fly off Durbin in the seventh.
NOTES: Phillies LHP J.A. Happ was placed on the 15-day disabled list with a strained forearm. LHP J.C. Romero was activated. RHP Nelson Figueroa will take Happ's next scheduled start Saturday at Arizona. ... Philadelphia 3B Placido Polanco did not start but was available off the bench after he was hit by a pitch on his left elbow Wednesday night. Dobbs started at third base. ... Atlanta's Troy Glaus was 0 for 4 with three strikeouts and is hitting .170. ... Werth, running toward the infield, made a tumbling catch in right field of a sinking liner hit by Diaz in the first inning.