The match went to penalties after the game was deadlocked at 0-0 after 120 minutes of football.
The hosts enjoyed most of the possession in the early stages of the first half, and looked to utilise the pace of Rodney Ramagalela down the right flank.
The Urban Warriors carved out the game's first chance after 29 minutes from a set-piece, but Mario Booysen directed his header off target.
The game opened up from there, and Ajax should have taken the lead in the 32nd minute when Tashreeq Morris was left one-on-one with George Chigova, however the striker failed to convert.
Stanley Menzo's charges carved out another opening five minutes later as Thabo Mosadi picked out Prince Nxumalo in the box, but Chigova produced another save.
Polokwane ended the half strongly and they nearly broke the deadlock before the break as Ramagalela was denied by goalkeeper Jody February from close range.
The second half was a contrast to the first, as both sides found it tough to create clear-cut opportunities.
That proved to be the tone for the majority of the second half as both sides lacked the killer instinct.
With 10 minutes remaining in the half, Bernard Molekwa withdrew Ramagalela for Mngomezulu as Rise and Shine pushed for a winning goal.
Neither side could get a winning goal in the closing stages, forcing the encounter into extra time.
Extra time continued in the same fashion as regulation time as neither club could fashion a clear-cut chances and the match went to a penalty shoot-out.
However, Rise and Shine managed to get the better of Ajax in the shoot-out to advance to the last eight.