Hudson (16-6) struck out four and allowed one unearned run to send the Braves back to Atlanta with a shot at winning an NL wild-card berth.
A year after a historic September collapse, the Braves are again close to a postseason spot. They can clinch during a six-game homestand that opens Tuesday.
The Braves were up 8½ games through Sept. 5 last year, but went 9-18 down the stretch and were overtaken by St. Louis on the final day of the season.
This season, the Braves can almost work the final week on setting their playoff rotation.
David Ross hit a solo homer for the Braves.
Craig Kimbrel worked a scoreless ninth for his 39th save.
The Braves had to listen to questions all season about how they would turn the page on their poor ending to 2011.
Looks as if they can answer with a champagne celebration at Turner Field.
The Braves have won seven of nine and 14 of their past 20 overall.
Hudson was on top of his game, allowing a single in the third and one in the fifth. His only mistake came in the sixth. Jimmy Rollins worked a leadoff walk, advanced to second on Hudson's errant pickoff attempt. Rollins scored on Chase Utley's sacrifice fly.
Cliff Lee (6-8) struck out 11 in eight strong innings, but lost for the first time since Aug. 11. Lee hadn't allowed more than a run in each of his past five starts and only one of his two runs allowed Sunday was earned.
The Phillies, though, are likely to miss the postseason for the first time since 2006.
The five-time defending NL East champions had won four in a row and 12 of 15 to get in the wild-card race, only to lose two straight to the Braves.
Manager Charlie Manuel said the Phillies had a "heartbeat" in the playoff chase. But their chances are about over.
Ross gave Atlanta a 1-0 lead in the second when his eighth homer of the year went over the wall in center.
The Braves loaded the bases against Lee in the third, getting one runner aboard when Lee bobbled a grounder, and Dan Uggla's sacrifice fly made it 2-1.
While the Braves handled the constant questioning about their meltdown with class, it's clear how much earning a spot in this year's field would mean. Considering last season's collapse, securing any playoff spot is quite the accomplishment. It would have been the biggest September meltdown in baseball history except that Boston blew a nine-game lead during the same month.
Notes: Lee had a double-digit strikeout game for the 23rd time in his career. ... The Braves (88-65) are 23 games over .500 for the first time since Sept. 9, 2011.