Qalinge scored his second Pirates goal in the 68th minute after Issa Sarr and Tokelo Langa cancelled each other’s goals out in the first half.
Pirates became the fifth Gauteng outfit to advance into the second round of the top-flight competition, having already made the final and lost in the season’s first cup competition, the MTN8.
It was a sluggish start from the hosts with City having the brighter start of the teams. Pirates had the first attempt in front of goal as Majoro was put through and unleashed a powerful effort, which goalkeeper Dino Visser did well to palm away.
The shot went a long way in settling Pirates down. The Buccaneers found their rhythm and soon looked threatening.
But Langa silenced the home crowd with his superb left-footed effort in the 15th minute against the run of play.
A failed clearance landed kindly for the midfielder, who swung his boot and directed the shot into the back of the net, taking a wicked deflection on the way in.
The visitors’ celebrations were short-lived, however, as Sarr rose above his markers and nodded home the equaliser for Pirates just three minutes later.
Level at the break, Pirates came out into the second period looking for the lead with header efforts from Mpho Makola and Majoro flying wide.
The Sea Robbers would not be denied 25 minutes before the final whistle as Qalinge swept home the winning goal, following wonderful build-up play and a superb assist from Majoro.
Having failed to deal with Polokwane’s opener, Pirates goalkeeper Senzo Meyiwa did a much better job in the 75th minute when he got two hands to a superb free-kick from Jabulani Maluleke to deny Rise and Shine the equaliser.