Grant Kekana netted an own goal, while Clayton Daniels and Dove Wome also scored for the visitors as SuperSport continued their winning run over their Tshwane rivals.
Vuyisile Ntombiayithethi saw red for the hosts in the 67th minute.
AmaTuks started the brighter of the two sides, but fell behind in the 20th minute through an unfortunate own goal from Grant Kekana. The former Matsatsanta right-back attempted to hack David Mathebula's cross away from danger, but only manged in putting the ball past his keeper.
Thuso Phala and Geofrey Massa both went close soon after before Kekana squandered a glorious chance to make up for his earlier error.
Khethukuthula Zwane played in a superb corner-kick, but Kekana could only manage to direct his header over Ronwen Williams crossbar from close range in the 39th minute.
Kekana's day went from bad to worse on the stroke of half-time.
The AmaTuks defender who was clearly frustrated with himself dove into a challenge inside the area, only succeeding in bringing down Dino Ndlovu.
Clayton Daniels duly stepped up and coolly slotted the ball past Washington Arubi, 2-0 at the break.
Massa looked to get the hosts back into the game and almost did pull one back for AmaTuks 55th minute. His free-kick beat the wall, but not an outstretched Ronwen Williams who pulled off a superb save.
Dove Wome extended SuperSport's lead, tapping in from close range in the 65th minute.
Vuyisile Ntombiayithethi then saw red following a dangerous tackle on Bafana Bafana fullback Sibusiso Khumalo in the 67th minute do completely dent the hosts chances of getting something out of the game.
Massa and Khumalo went close at either end in the final 10 minutes. The Uganda international forcing Williams into a good save while Khumalo's thunderous effort from range sailed just wide.
The win moves SuperSport up to fifth place on the log while AmaTuks slip down to 14th.
Scorers:
University of Pretoria (0) 0
SuperSport United (2) 3 (Kekana OG 19'. Daniels 45' pen, Wome 65')
Teams:
University of Pretoria: Arubi; Kekana, Shoyisa, Jaure (Monyai 37'), Nzimande, Mosadi (Mnyamane 74'), Ketjijere, Ntombiayithethi, Ngubane, Zwane (Mukamba 62'), Massa
SuperSport United: Williams; Moloi, Daniels, Teyise, Khumalo, Mathebula (Mokeke 57'), Morton, Wome (Chapman 71'), Phala, Manyama, Ndlovu (Nxumalo 59')