Michael Gumede returned for Arrows in the place of Sibusiso Sibeko, as Jabulani Maluleke and Sibusiso Mbonani sat out for City through a bout of injuries.
Arrows launched the first chance of the game four minutes in as Knox Mutizwa brought the best out of George Chigova who parried from a corner following a close-range shot.
The home side continued threatening, as the visitors struggled to get a look in up front despite a few promises from Mohammed Anas and Puleng Tlolane.
Bongile Booi entered the field for Tlolane 12 minutes in the second half after the latter pulled a hamstring on the far side of the area.
Rise and Shine looked threatening on the counter-attack and that nearly paid dividends on 66 minutes but Anas and Themba Chauke weren't on the same wavelength.
Mutizwa seemed destined to break the deadlock from a free-kick on 70 minutes, but Chigova pulled off an acrobatic save to keep his side in the contest. At the other end, Edmore Sibanda was brought into action for the first time as he smothered Wiseman Maluleke's snap shot four minutes later.
Chances continued falling to either side, as Lindokuhle Mtshali cracked the woodwork on 79 minutes and Sibanda saving off Booi a minute later. Arrows pushed for the winner towards full-time, but Chigova's heroics led the match to extra time instead.
Abafana Besthende seized control five minutes in extra time when Nicholas Motloung fired into his own net whilst attempting a defensive clearance.
The visitors failed to respond and fall to their third straight defeat across all competitions, whilst Arrows march to the last eight.