Thabo Mnyamane had the first shot of the game after five minutes after being allowed to stride towards the Black Leopards goal, but his effort lacked the power to trouble King Ndlovu.
TTM had the ball in the back of the net minutes later but the goal was ruled out for a foul on Ndlovu as he took a boot in the face after dropping Mnyamane's free-kick, leaving Mogakolodi Ngele to sweep home.
Both sides were playing some good football but TTM were the more attacking of the two, and came close to a second when Ngele headed over the target from point-blank range following an excellent cross from Lebohang Mabotja on 13 minutes.
Onyedikachi Ononogbu fired in a volley that was well saved by Washington Arubi with 23 minutes on the clock as Leopards tried to stamp their authority on this game.
TTM were putting the home side under all sorts of pressure and were deservedly in the lead when Ndlondlo stole in on the left-hand side to score an excellent goal, with a deft touch into the bottom right-hand corner of the net.
Arubi kept his side ahead with a superb save from a belter from Edwin Gyimah inside the 18-yard area after TTM struggled to clear their lines following a free-kick late in the first half.
Both sides came out firing in the second period with Ngele hitting the crossbar with a long-range for the home side shot before Ononogbu fired just over at the other end.
TTM continued to attack through Mnyamane, who hit his 52nd minute free-kick just over the target, before Anas went close again with a header from the centre of the box as Ononogbu floated in a set-piece
Gyimah was guilty of a missed header of his own before a seemingly massive chance for Leopards to level when the ball fell to substitute Rodney Ramagalela - but he couldn't direct his effort goalward, only to be called up for offsides.
Despite efforts from both sides to find a goal in the second half, it was TTM who were to extend their lead from the penalty spot on 83 minutes as Ndengane smashed into the bottom left-hand corner of the net for his third goal in as many games.
Ovidy Karuru was almost in with an acrobatic effort with the match winding down but time was always against the home side after conceding a second goal, as TTM celebrated a deserved win and their passage to the semi-finals of this lucrative competition.
Leopards: Ndlovu, Makobela, Mashoene, Matsimbi, Gyimah, Makgetlwa, Mthethwa, Ononogbu, Anas, Hlongwane, Karuru.
Subs: Mendes, Masia, Abubakar, Mokoena, Thutlwa, Maluleke, Ramagalela, T.Ndlovu.
TTM: Arubi, Lukhubeni, Ndengane, Mabotja, Nonyane, Madhanga, Ngele, Mnyamane, Lamola, Timm, Ndlondlo.
Subs: Mhlongo, Manzini, Thopola, Rakhale, Nevhulamba, Manaka, Mphambaniso, Masegela, Nkili.