Andre de Jong opened the scoring for the Betway Premiership side from the penalty spot after just 10 minutes of the match.
Thalente Mbatha added a deflected second goal on 17 minutes but TTM were back in the game six minutes before the break from Sithembiso Ngobe.
Hal-time substitute Patrick Maswanganyi needed just five minutes to restore his side's two-goal cushion before setting up Sipho Mbule for a super strike on 90 minutes.
Reflecting on the game, Man of the Match Mbatha explained the influence of their head coach during the break.
He said on SuperSport: "Coach told us at half-time that we're bringing them into the game, and we must come back and score two goals for us to secure this game.
"So, I believe that also the words the coach gave us in the change room and the words of encouragement that pushed us to come and continue."
Mbatha added: “As you saw, that, the impact players came in and changed the game. 'Tito' [Patrick Maswanganyi] scored and assisted, so, for us it's all about attitude and mentality to keep going.”
Orlando Pirates head coach Abdeslam Ouaddou has called on his side to be more ruthless after a 4-1 victory over Tshakhuma Tsha Madzivhandila in their Nedbank Cup last 32 encounter.
Orlando Pirates produced a ruthless attacking display to secure a convincing 4-1 victory over Tshakhuma Tsha Madzivhandila in their Nedbank Cup Round of 32 clash at Moses Mabhida Stadium on Saturday.
Orlando Pirates coach Abdeslam Ouaddou believes the club's pursuit of a historic clean sweep has been powered by trusting local talent.
Orlando Pirates get their Nedbank Cup campaign up and running away to 2021 champions Tshakhuma Tsha Madzivhandila at the Moses Mabhida Stadium on Saturday.
