The deadlock was broken early into proceedings by Morgan Gould but the hosts cancelled out the big defender's goal just before the half-hour mark through Tshepo Tema.
The second-half started off in great fashion as Jeremy Brockie handed Matsatsantsa the lead just before the hour mark, but Vusimuzi Mngomezulu quickly had City back in the tie five minutes later.
Thuso Phala then sealed the victory with less than 15 minutes to play, as the hosts failed to take their chances in front of goal.
The visitors got off to pretty much the perfect start as SuperSport starlet Tebogo Mokoena whipped in a peach of a cross that Gould powered home via his head.
Jeremy Brockie could have had his side further in front minutes later as he drilled a shot towards the far post from a tight angle but George Chigova got a strong hand to the New Zealander's effort.
In similar fashion to the manner in which they conceded City almost found their equaliser as Maluleke's excellent ball into the box found the head of Rodney Ramagalela but he couldn't find the target.
Eventually parity was restored as a cleverly worked set-piece freed Simphiwe Hlongwane on the left and his cross was nodded past Ronwen Williams by Tema in the 29th minute.
In the closing stages of the first stanza Ramagalela was played clean through but failed to get the better of Williams, the stopper diving at his feet to deny the striker before Mngomezulu skewed the follow-up effort wide.
Brockie did eventually get his side in the lead in the 58th minute as he volleyed home in stunning fashion from an acute angle.
However, the lead was short-lived as Mngomezulu drew level once again after just five minutes.
United took the lead for the third time in the encounter, as Phala got onto the end of a good exchange of passes between Mandla Masango and Reneilwe Letsholonyane, before blasting home from inside the box in the 77th minute.
Edgar Manaka then had a great opportunity to level the score once again, as Maluleke picked out his teammate's run into the box, but Williams made a wonderful one-handed block to keep his side ahead.
In the final minute of regulation time, Brockie was away on a counter-attack before picking out Thabo Mnyamane on the edge of the box, but the latter failed to capitalise after his first touch let him down.
The visitors managed to hold on to record their first win in three games, moving to within nine points of leaders Bidvest Wits, who have a game in hand.