With the score tied 4-4 in the 12th, Justin Upton coaxed a leadoff walk from Jake Diekman (0-2) and went to second on Freddie Freeman's groundout. Evan Gattis was intentionally walked to get to Paul Janish, but he also succeeded in drawing a base-on-balls.
Justin De Fratus took the mound and Uggla sent a squibber to shortstop. Janish was out at second but Uggla hustled to beat the relay throw to first as Upton crossed the plate with the decisive run.
Luis Avilan (4-0) was credited with the victory and Craig Kimbrel racked up his 33rd save as the National League East-leading Braves rattled off a ninth straight win.
Upton had a solo homer and scored three times while Freeman drove in a pair of runs for Atlanta.
John Mayberry smacked a two-run homer for the Phillies, who stumbled to their 12th loss in 13 games.