After a goalless first half, Stars took the lead in spectacular fashion through Fikru Tefera, only for Reneilwe Letsholonyane to equalise before Parker’s winner.
In a slow first half, Chiefs came closest to opening the scoring on 20 minutes when Tsepo Masilela fired wide.
Amakhosi should have netted first just before the break, but Kingston Nkhatha headed wide from close range.
It looked like Chiefs were going to pay for their profligacy when Tefera gave Stars the lead on 55 minutes with a clinical finish from the edge of the box.
However, Chiefs levelled on 77 minutes through Letsholonyane, before Parker netted with a free-kick to hand his side the win.