Brazilian centre back Ricardo Nascimento scored the only goal in the 83rd minute to hand Sundowns a first ever success in the Super Cup, being played for the 25th time.
Mazembe's goalkeeper Sylvain Gbohouo stood between Sundowns and a runaway score as the home side ran riot with possession and chances but were unable to find the net.
Liberian international Antony Laffor had the best of the opportunities but will be pleased to see the back of 32-year-old Gbohou.
In the very first minute, Sundowns caught Mazembe midfielder Daniel Adjei in possession and were away on goal with Themba Zwane's shot striking Joel Kimwaki on the hand but the Egyptian referee Ghead Grisha turned down an appeal for a penalty.
Nascimento might have got the opener in the sixth minute but powered his header wide and then was guilty of a horror mistake at the other end that almost cost the hosts.
He allowed a ball to bounce over his head in a vain effort to catch Mazembe offside but got his calculations all wrong to allow Mazembe striker Ben Malongo away at goal with just Sundowns' goalkeeper Denis Onyango to beat.
Malongo struck the upright with his initial effort only for the ball to run back to him and offer him a second chance, which he also hit against the post to the great relief of the Sundowns' supporters.
After that it was Sundowns' Liberian international Anthony Laffor who put his stamp on the game with mazy runs that sought to unsettle the Congolese defence.
Laffor set up Khama Billiat for a shot that sliced off the side of the boot in the 37th minute and then three minutes later again provided Billiat with a chance, which Gbohouo blocked.
Laffor, who turned 32 on Friday, had a shot of his own from outside the area on the stroke of half-time that almost slipped under Gbohouo's body only for the Ivory Coast international goalkeeper to stop it creeping over the line and emerging with a broad smile of relief.
In the second half, Mazembe looked to be battling with the altitude and tiring visibly. They brought on former pin-up boy Tresor Mputu to the delight of their supporters as he returns to the club after a lengthy Fifa ban and a spell playing club football in Angola.
Sundowns' two defensive midfielders both had chances around the hour mark with Tiyani Mabunda almost bursting through but then being forced wide and Hlompho Kekana hitting a powerful shot straight at Gbohouo.
Laffor then had a glorious chance in the 66th minute as veteran Mazembe defender Jean Kasusula gave away the ball but bearing down on goal Laffor hit the ball over when it seemed easier to score.
Mabunda and Tau then scythed open the Mazembe defence in the 69th minute but Gbohouo made a good stop to deny a dominant Sundowns.
But the save of the match came in the 77th minute when a five man move carved up the Mazembe backline with Laffor having his close-in shot brilliantly stopped.
The breakthrough finally came in the 83rd minute when Sundowns got a penalty for a wild challenge by Issama Mpeko on Kekana just when the home captain looked to have lost the ball.
Nascimento stepped up to send Gbohouo the wrong way and finally give Sundowns the lead they deserved.