The Brazilians took the lead on 35 minutes through Themba Zwane, who deflected Tebogo Langerman's long-range effort past Washington Arubi.
AmaTuks were level on 72 minutes when a lapse in defence allowed Geoffrey Massa to fire a volley past Kennedy Mweene.
But just before halftime in extra-time, Pelembe produced some magic in the area, controlling Cuthbert Malajila's flick-on before beating one defender and firing a stunner past the goalie.
Tuks were quickly on the back foot as Sundowns applied heaps of pressure on their cross-town rivals.
Arubi proved to be the only man able to thwart the home side. He was often the last line of defence against a Downs team looking threatening with every touch of the ball.
Cuthbert Malajila had a fierce volley saved, while Teko Modise’s shot from a tight angle was also parried.
But Sundowns would not be kept out for long; Langerman sending the home side ahead after 36 minutes with a seemingly wayward shot from distance.
The effort, however, took a nasty touch off Zwane, which caught the Zimbabwean goalkeeper off-guard and allowed the ball to trickle into the back of the net.
Tuks had a much more positive start to the second half and managed to keep Sundowns on the back-foot.
Substitute Massa looked lively from the moment he got onto the field and eventually silenced the home crowd on 72 minutes when poor defending on the edge of the area allowed the striker to put his foot through the ball and thunder home past Kennedy Mweene, who hardly had a save to make up to that point.
The game settled down as the clock wound down and soon referee Robert Smith signalled the end of 90 minutes, meaning extra-time.
Tuks were hoping to keep Sundowns at bay for as long as possible, but eight minutes into extra-time, Pelembe grabbed the winner with a superb touch and turn to send Pitso Mosimane’s men into the quarters.