It was Jones' first three-homer game in a six-year career. He has 11 multiple-homer games lifetime, including five this season and three this month.
Jones didn't get an opportunity to hit a major league record-tying fourth homer when Chipper Jones grounded out to end the ninth inning.
The last Braves player to hit three homers in a game was Jeff Blauser against Chicago in 1992.
Andruw Jones tied it at 1 with a homer in the second inning and made it 3-1 with another solo drive in the fourth. He hit his 35th homer, a two-run shot in the eighth.
Damian Moss (12-6) allowed one run and five hits in 6 2-3 innings to win for the sixth time in seven decisions.
The NL East champion Braves moved five games ahead of Arizona in the race for homefield advantage throughout the playoffs.
Philadelphia, seeking its second consecutive winning season for the first time since 1982-83, fell to .500 with four games remaining.
Phillies rookie Brett Myers (4-5) gave up four runs and six hits in five innings.
The Braves took a 2-1 lead in the third when Matt Franco grounded into a double play with the bases loaded.
Marcus Giles started the inning with an infield single and went to second on a fielder's choice when first baseman Dave Hollins made a bad throw to second on Moss' bunt. Rafael Furcal reached safely when third baseman Placido Polanco committed a throwing error on his bunt attempt. Franco's double-play grounder to second scored Giles.
Vinny Castilla's double-play grounder in the fourth made it 4-1. After Jones homered off the backdrop in left-center, Darren Bragg and Javy Lopez hit back-to-back singles to put runners on first and third. Bragg scored on Castilla's double-play grounder to third.
Polanco gave the Phillies a 1-0 lead in the first with his ninth homer — a shot off the facing of the upper deck in left field.
Moss escaped trouble in the third inning by getting Pat Burrell to ground into a double play with the bases loaded.
Dan Plesac walked Chipper Jones with one out in the eighth. Jose Santiago entered, and Jones lined a 1-1 pitch deep to left-center field.
Pinch-hitter Keith Lockhart's RBI single in the ninth provided the final margin