Umoya squandered a big chance to take an early after Katlego Otladisa shot straight at Ludwe Mpakumpaku from possession turnover after just three minutes.
Nevertheless, United were first off the mark in the 15th minute as Otladisa, on loan from Mamelodi Sundowns, nodded home Brandon Theron's cross.
Galaxy made a change nearer to halftime, with Bathusi Aubaas coming on for Siphelele Ndlovu to shore up their defensive stall at the midway point of the first half.
Just before the halftime break, United conceded a penalty after Roscoe Pietersen handled inside the area, allowing Zakhele Lepasa to blast home and level matters on the night.
The home side pressed for an immediate way back, but Mpakumpaku palmed Otladisa’s close-range effort out for a corner shortly after the restart.
Umoya coach Dominic Isaacs brought on his first change in Nathan Paulse for Otladisa after 61 minutes, with the home side looking to restore their lead.
Dino Visser came to the home side's rescue with a couple vital saves to keep out Snethemba Ngidi’s and Zairon Abrahams before the 75th-minute mark.
Within the final stages, the visitors got their reward after Sizwe Mdlinzo found the back of the net with an unorthordox volley that sailed into the top corner to seal the victory.
Umoya: Visser, Theron, Chipeta, Pietersen, Tshabangu, Mekoa, Maart, Matlou, Otladisa, Senne, Hammers.
Subs: Salie, Nkewana, Kamatuka, Losper, Paulse, Letsie, Saralina.
Galaxy: Mpakumpaku, S. Ndlovu, Dube, Mashego, Nyama, Lepasa, Ngidi, Boooibe, Nduli, Mdlinzo, N.Ndlovu.
Subs: Shangae, Modiba, Phungwayo, Mashifana, Abrahams, Chaine, Aubaas.