Pirates came without Luvuyo Memela, who failed a late fitness test and was pulled out a competitive team.
It was a long-awaited return for Thabo Qalinge after a month on the sidelines, as Augustine Mulenga earned his debut start.
Zambian Justin Shonga got the first shot on goal, but it was straight at Sage Stephens in the opening exchanges.
Shonga unluckily struck the post after chasing down the Citizens back-four minutes later, while City responded with an attack of their own as Ayanda Patosi forced Siyabonga Mpontshane into a fine save,
Roland Putsche went close again after a header from a free-kick, but Mpontshane was able to keep it out, despite the pressure.
Taariq Fielies fired another shot from a free-kick for the home side, but like the previous others, it failed to trouble Mpontshane.
Zimbabwean-born Marshall Munetsi, deployed in an unfamiliar defensive role, found space in attack but was unable to find the target as the sides went into the break scoreless.
The Citizens drew first blood after a shot from Ayanda Patosi found its way past Mpontshane from Surprise Ralani’s cross on 55 minutes.
It led the Buccaneers to two instant changes from the bench, with Thabo Matlaba and Bernard Morrison replacing Qalinge and Mulenga.
It almost looked like an inspired change when Morrison came within a whisker of finding the equaliser, but it took an unlikely character in Teko Modise to stop the effort from crossing the goal-line.
Thembinkosi Lorch was looking to celebrate his national call-up with a goal, but after connecting with a cross from the right, failed to find the net.
Goal-scorer Patosi made way for the industrious Thabo Nodada, while youngster Lyle Foster replaced Lorch in the closing stages.
The Citizens managed to see off a late surge from the visitors to book their spot in the last eight for the first time in their history.