Iqraam Rayners was given his Matsatsantsa debut as Bongani Khumalo made a rare appearance. Meanwhile, Tshakhuma gave Justin Shonga and Nicholus Lukhubeni amongst others their season debuts while only three players were named on their bench.
United made a dream start when Bradley Grobler spotted Ghampani Lungu's delivery eight minutes in to beat Tshakhuma goalkeeper Brighton Mhlongo from close-range.
SuperSport doubled their tally two minutes to the half-hour mark after Rayners showed quick footwork before cracking the top of the net to make up for his big miss earlier in the half.
It was three inside the closing minutes of the first half as Lungu drifted towards the shoulder of the defensive area for a right-footed finish after carving an opening.
Tshakhuma regained confidence a minute to halftime and halved the deficit when a sumptuous left-footed strike from Mogakolodi Ngele left Ronwen Williams stranded.
A double substitution from Matsatsantsa right after the break saw new boy Lucky Mohomi given and youngster Keenan Phillips handed their official debuts.
Matsatsantsa should've made it four 52 minutes in, but Mhlongo dived across to smother Lungu from the back-post with Teboho Mokoena skiing over a sitter minutes later.
United started to feel the heat four minutes later when Ngele jumped at the near post to head home a corner-kick for his and his team's second of the day.
Tshakhuma began oozing confidence with the closing stages on the horizon, as Shonga brought Williams to a point-blank save following a snap-shot.
Kaitano Tembo's side tried easing the nerves through a glancing header from Clayton Daniels late on, but had done just enough for the win and a place in the semi-finals.
TTM: Mhlongo, Lukhubeni, Nkili, Nonyane, Theron, Timm, Maphangule, Ngema, Lamola, Ngele, Shonga.
Subs: Arubi, Manaka, Monyamane.
SuperSport: Williams, Daniels, Kekana, Khumalo, Bhasera, Mokoena, Rayners, Lungu, Gabuza, Grobler, Webber.
Subs: Pule, Chigova, Moralo, Mathebula, Ndhondhi, Phillips, Mbule, Appollis, Mohomi.