Pirates were on top go their game from start to finish as Kermit Erasmus' hat-trick steered the Buccaneers ship into the next round with a 5-2 aggregate win after the away leg ended 2-2.
Sifiso Myeni was also outstanding on the night, setting up two of Erasmus' goals, with Thamsanqa Gabuza assisting the other.
Bucs missed two good chances to score before the floodgates opened, with Erasmus forcing Mounana goalkeeper Bitseki Moto into the first diving save of the match after good work by Matlaba, before the roles were reversed and the left-back missed a big chance from Erasmus' cutback.
But there was nothing Mounana could do when Erasmus opened the scoring in the 24th minute, tapping in after Myeni won the ball, played a one-two and put it on a plate with a low cross from the right.
Four minutes later it was 2-0 as Myeni produced a sublime pass from the centre of midfield with the outside of his boot to Erasmus, who rounded Bitseki and slotted home on his left foot from a tight angle, a superb finish.
Pirates created more chances to add to the scoreline and were duly rewarded with a third goal in the 56th minute as a swift counter-attack started by Issa Sarr and helped on by Gabuza ended with Erasmus taking one touch to put Bitseki on the floor, before slotting home for his hat-trick.
Eric Tinkler brought on Lehlohonolo Majoro and Thabo Rakhale in the last 25 minutes and Majoro nearly made an immediate impact, trying to catch Bitseki off his line with a first-time shot but the keeper made a world-class save to deny him.
The home side comfortably saw out the remainder of the game to ensure their passage further into Africa.
Pirates XI: Mhlongo, Jele, Matlaba, Sangweni, Nyauza, Sarr, Manyisa, Makola, Myeni (Rakhale 74'), Gabuza (Majoro 64'), Erasmus
Subs: Zikalala, Gcaba, Phungwayo, Masalesa, Rakhale, K Masuku, Majoro
Mounana XI: Bitseki, Ndongnba, Ambourovet, Nkoume, Diouf, Massanba, Ness, Ovedraogo, Ondo, Guedegbe, Ndong