The Buccaneers would have been wary of their opponents having lost, ironically, 4-1 to third-tier Maluti FET College in 2013, one of the most famous results in the country’s knockout football history.
Pirates made a fast start to the game at Moses Mabhida Stadium as new signing André de Jong scored his first goal for the club from the penalty spot.
It was 2-0 inside 17 minutes when Thalente Mbatha’s long-range strike took a wicked deflection and settled in the net.
TTM fought back and did score as former Chippa United and Cape Town Spurs left-back Sithembiso Ngobe found the back of the net.
But Pirates took control again in the second half as Patrick Maswanganyi restored their two-goal advantage and then set up a goal for Sipho Mbule to make it 4-1.
Mbule came off the bench for his first minutes since the Africa Cup of Nations finals in Morocco.
Second-tier Upington City caused the first shock of the Nedbank Cup when they defeated topflight Magesi FC on penalties following a 0-0 draw at the Mxolisi Dicky Jacobs Stadium.
It was an unfortunate outing for new Magesi signing Levy Mashiane, whose missed penalty in the shoot-out proved decisive.
Jacksa Spears became the second ABC Motsepe League side into the Last 16 after defeating fellow third-tier outfit FC Cardinals 4-2 after extra time in Bethlehem.
Bokamoso Seretsi and Sheldon Mashuge had Spears 2-0 up with five minutes to play before Cardinals sparked a remarkable comeback.
First, Katleho Tshabalala converted a penalty on 85 minutes, before Kgotso Mizi sent the game into extra time. But a brace from Moeti Mofokeng turned the tie back in favour of the Northern Cape visitors.
Spears are making their second Nedbank Cup appearance, having lost in the Last 32 in 2013.
Striker Bradley Majola scored his first goal for Sekhukhune United following a January move from Stellenbosch FC as they edged second-tier Highbury FC 1-0 in Gqeberha.
The tight tussle was settled after 11 minutes as Majola netted from a Tresor Yamba assist.
Sekhukhune United coach Eric Tinkler has made winning the Nedbank Cup a major focus for the side this season and they are off to a good start. The club lost the 2023 final to Pirates.
Thuso Mogale scored twice and Ofentse Kgosana added the other as second-tier Casric Stars defeated North West ABC Motsepe League side Army Rockets 3-0 in Rustenburg.
The fixture between Lamontville Golden Arrows and Orbit College was postponed after being initially delayed by lightning. Abafana Bes'thende led 1-0 thanks to Lungelo Nguse's 28th minute penalty.
A new date will be announced by the Premier Soccer League in due course.