The Phillies scored twice in the eighth and ninth for their second come-from-behind win in as many days, They have won four of five to improve to 4-3 under Ryne Sandberg, who became the interim manager when Charlie Manuel was fired on Friday.
Colorado carried a 4-3 lead into the ninth, but Rafael Betancourt (2-5) blew a save opportunity for the second straight game and the third time in 19 chances.
Jimmy Rollins started the winning rally with a two-out double. He then stole third and scored on Michael Young's slow roller to third that went for a hit. Young had the game-winning hit off Betancourt in Philadelphia's 4-3 win on Wednesday night.
Betancourt departed after Young's at-bat with an apparent injury, heading to the dugout after a visit from manager Walt Weiss and a trainer. The right-hander had lunged for Young's grounder that went just out of his reach.
Jeff Francis came in and walked Chase Utley before Brown's grounder to right scored Young. Brown was mobbed by the Phillies, who took three of four games from the Rockies for just their second series win since the All-Star break.
Cesar Jimenez (1-0) pitched a scoreless ninth for the victory.
Willin Rosario homered for Colorado, which has dropped five of six. The Rockies have won nine of 39 games against Philadelphia since the start of the 2008 season.
Darin Ruf homered and Carlos Ruiz had three hits for the Phillies.
Colorado rookie Chad Bettis allowed one run and six hits over 5 1-3 innings in his fifth career start. He was in line for his first win before Philadelphia's late rally.
Cody Asche doubled home a run in the second for Philadelphia, but Dexter Fowler had a tying sacrifice fly in the fifth. The Rockies then scored three runs in the sixth on four straight hits, chasing right-hander Kyle Kendrick.
Rosario had the big blow, a line drive to left for a three-run shot. It was the third homer in the last four games for Rosario, who extended his hitting streak to 13 games.
The Phillies pulled within one on Ruf's two-out, two-run homer off Matt Belisle in the eighth.
Kendrick continued his recent struggles. The right-hander avoided his third straight loss, but he gave up four runs and eight hits in five-plus innings, raising his ERA to 8.14 in his last six starts.