Stars took a 2-1 lead in extra-time through Stephen Tau, but Andile Mbenyane scored an important Chippa equalising goal to ensure that the match went into a penalty shootout.
Chippa booked their place in the Last 16 after winning on penalties and their coach Dan Malesela will be hoping to win his second Nedbank Cup trophy, having won his first with TS Galaxy in 2019.
Meanwhile, Swallows FC secured a 1-0 victory over Cape Umoya United in a match which was played at Dobsonville Stadium.
The score was 0-0 at the interval after the NFD side contained Swallows in the first-half with Kgaogelo Sekgota having missed a sitter.