Collen Makgopela netted for Stars, while John Maduka and Carlo Scott scored for Celtic.
Stars took the lead in the 11th minute when Makgopela headed home from Tshepo Ramokala’s cross.
Siphesihle Ngobese had three shots saved by Stars keeper Wayne Sandilands in the space of 10 minutes, before Koketso Mmotong saw his effort well saved by Celtic keeper Shuaib Walters in the 36th minute.
Celtic were awarded a penalty in the 40th minute when Bekithemba Ndlovu fouled Patrick Malokase inside the area and Maduka slotted home with ease.
The match remained 1-1 at the break.
Celtic took the lead in the 76th minute when Carlo Scott slotted home from close range after receiving a pass from Timothy Batabaire.
Maduka also threatened late on with a long range effort that was saved by Sandilands.