The only goal of the game came with five minutes remaining - Nigerian defender James Okwuosa slotting the ball past his own keeper.
Dikwena had an early chance through Eleazar Rodgers, but he shot well over on seven minutes.
Chippa looked certain to score 10 minutes later when Mpho Mvelase found himself one-on-one with Kabelo Dambe, but the keeper easily came out on top.
David Zulu though he had scored just before the break, only to see his shot cleared off the line by Luvolwethu Mpeta.
Zulu came close again just past the hour-mark with a long-range effort, before striking the crossbar from a tight angle.
Against the run of play, Stars got the deciding goal five minutes from time when Okwuosa deflected Mahlatse Makudubela’s cross past his keeper to send the champs through to the quarterfinals.