The Pirates scored four times during the game's final three innings to overcome a 3-1 deficit and win for the fifth time in six games.
Pedro Alvarez hit a solo homer for the Pirates in the seventh to bring them within one and they jumped in front one inning later by putting their first five batters on base.
Jose Tabata drew a leadoff walk against reliever Mike Adams (1-2) and Starling Marte then reached on an infield single. A base hit to right by Travis Snider delivered Tabata with the tying run and Andrew McCutchen walked to load the bases.
Jeremy Horst relieved Adams and was greeted by a single from Inge that scored Marte.