Sipho Jembula struck deep into stoppage-time to cancel out Tashrique Morris's first-half opener for the Urban Warriors.
The visitors made the better start in the Mother City and threatened twice inside the opening five minutes, with Jabu Maluleke coming closest with a free-kick that flew into the side-netting.
But it was Roger de Sa's side who took the lead on 17 minutes with their first real attack of note, Milton Ncube breaking away down the left flank before crossing for Morris to open the scoring from close range.
Rise and Shine looked for a swift response but they were let down by poor finishing, with Puleng Tloane guilty of wastefulness on 28 minutes when he beat Abbubaker Mobara to create space for a shot but curled the ball wide of goal from 14 yards out.
The home team then had two good chances to extend their lead as the first half wore on, Morris shooting straight at goalkeeper Modiri Marumo from point-blank range on 32 minutes, before the striker played a mis-placed pass to Bantu Mzwakali three minutes to the break when he should have taken a strike at goal.
Morris tested Marumo again early in the second half, although he should have done better with his 52nd-minute effort from Cecil Lolo's cross after the Cape outfit had broken through the City defence.
Lolo then found himself in a goal-scoring situation moments later after the Polokwane defence had been exposed again, but his shot from inside the area was blocked and the danger cleared.
But the game entered a lull after the two early opportunities as both teams struggled to find their rhythm in the second stanza, with chances on goal at a premium.
And just when it appeared as though the Urban Warriors had done enough to claim a first win in seven matches, Rise and Shine found an equaliser right at the death.
Ajax keeper Anssi Jaakkola could only parry Maluleke's free-kick and Jembula was on hand to scramble the ball over the line to earn City a share of the spoils.