The Phillies trailed 4-1 heading into the eighth, but scored twice in each of the last two innings to win for the fourth time in five games. That run of success has followed a stretch in which Philadelphia lost seven out of eight.
Wilin Rosario hit a three-run homer in the sixth to give the Rockies a three-run cushion, but the Phillies closed within one in the eighth on a two-run blast from Darin Ruf.
Rafael Betancourt (2-5) came on in the ninth for the Rockies and for the second straight night blew a save opportunity.
He retired the first two batters he faced, but then gave up a double to Jimmy Rollins.
Rollins stole third and scored the tying run on an infield single by Young. After Chase Utley drew a walk, Brown drove a single to right to end the game.
The comeback gave the win to Cesar Jimenez (1-0), who won for the first time in a four-year career made up of 45 relief appearances and three starts with Seattle and the Phillies.
Jimenez struck out one while retiring the side in order in the top of the ninth.