The Team of Choice took the initiative to attack in the opening exchanges while City were content at sitting back and looking for chances on the break.
In the 19th minute, Siphelele Mthembu had a chance to open the scoring for the Citizens with a strike from just outside the box, but his effort missed wide.
Mthembu squandered another chance for Benni McCarthy’s charges in the 27th minute by blazing over the crossbar with only goalkeeper Richard Ofori to beat.
Fadlu Davids’ men had a good attacking spell after 35 minutes, but the Citizens were firm at the back to deny the hosts any openings.
Keanu Cupido eventually broke the deadlock for the Citizens on the stroke of halftime with a header at the back post.
Mohau Mokate almost equalised for United just after the break with a header from inside the edge of the box but his effort sailed slightly wide.
The hosts were increasing their intensity towards the hour-mark but they rushed their moves upfront and struggled to mount any serious attempts at goal.
The match was getting ugly with a quarter of an hour remaining, with tackles flying all over the pitch, much to the displeasure of McCarthy, who lost Mthembu and Thamsanqa Mkhize.
Maritzburg were pressurising the Citizens in the closing minutes, but the visitors managed to hold on to march into the semi-finals of the competition.