Galvis' home run was his second game-ending shot this season.
"A walk-off home run is the best feeling," Galvis said.
Galvis was recalled Sept. 2 from triple-A Lehigh Valley after beginning the season with the Phillies. He said getting regular at-bats in the minors was beneficial.
"I kept my head up and wasn't sad when I went down," Galvis said. "It helped me a lot."
Phillies righthander Kyle Kendrick, in the midst of a career-tying four-game losing streak, had a solid outing, allowing three runs in six innings and tying a career high with eight strikeouts.
He stood to be the winner, but Jonathan Papelbon allowed a two-out, two-strike, two-run home run to Andrelton Simmons to tie the score at 5-5 in the ninth inning.
Carlos Ruiz also continued his late-season surge for the Phillies. Ruiz, who had a .933 on-base-plus-slugging percentage in August, went 2 for 4 with three RBIs.
Atlanta first baseman Freddie Freeman, who is mounting a late MVP campaign, opened the scoring with a two-run single in the third.
Ruiz tied the score with a two-run single in the bottom of the inning.
In the fifth inning, Chase Utley was charitably awarded a double even though his base hit to left was bobbled by Evan Gattis, who looks like a catcher playing the outfield, which he is.
Utley scored on Ruiz's RBI double to left.
Galvis made it 4-2 with an RBI single up the middle, chasing Braves starter Alex Wood.
The Braves cut the lead to 4-3 on Chris Johnson's RBI double past a diving Hernandez in center in the sixth.
Kevin Frandsen's RBI single in the eighth inning gave the Phillies their fifth run.
Caution on Brown
Interim manager Ryne Sandberg said he expected Domonic Brown to return from his sore left Achilles tendon before the season ends Sept. 29, but there is no timetable. Brown's last appearance was as a pinch-hitter Sept. 1 in a 7-1 loss to the host Chicago Cubs. According to Sandberg, Brown won't return until he is free of pain.
In a Friday video interview with The Inquirer, Brown said he was feeling better, but agrees with the cautious view. "I want to play, but want to be smart at the same time," Brown said.
Brown said he expects to return, but like Sandberg has no set time.
Howard, Revere to Fla.
Ryan Howard, who had left-knee surgery July 10, and Ben Revere, out since July 13 with a broken right foot, will participate in the Florida Instructional League. The games will be staged Sept. 23 to Oct. 11.
Howard is in Clearwater rehabbing his injury and Revere will depart for there when this current Phillies homestand ends after Thursday's game with the San Diego Padres. Revere said he has been jogging.
"There is still a little bit of pain but nothing too serious like before," Revere said.
Contact Marc Narducci
at email@example.com. Follow on Twitter @sjnard.