Esperance scored on either side of half-time through Anice Badri and substitute Haythem Jouini as they condemned Pirates to their first defeat in Group B.
The hosts probed early on as Wayne Sandilands was forced into a save in as early as the sixth minute, with a headed effort sent towards his goal.
10 minutes later Youcef Belali neatly picked out Badri from a set-piece, with the winger making no mistake to slot home with a low shot from an acute angle after beating his marker.
The Bucs were in a spot of bother as Mntambo lost possession in a dangerous area in midfield, as Esperance broke on the counter but ultimately saw a shot blocked with numerous bodies on the line.
Alfred Ndengane was forced to clear off the line on the half-hour mark as a floated effort at goal caught Sandilands scurry across his line in trying to reach it.
The defending champions closed the half on a high as they forced a good save from Sandilands following a threatening ball that picked out Chaalali who fired towards goal from close range.
Bucs through on Thamsanqa Gabuza at the start of the second half as they looked to add impetus to their attack that proved rather blunt in the first stanza, but he could do little to threaten Rami Jeridi.
The inclusion of Justion Shonga eventually seemed to affect the game as Milutin Sredojevic threw numbers forward in attack, with a further inclusion of Kudakwashe Mahachi.
Meanwhile, Sandilands was kept busy at the back as Happy Jele and Alfred Ndengane put in a rather underwhelming performance with Mohamed Yaacoubi forcing numerous saves from Esperance corners.
The home side eventually capitalised on their continued dominance as a long ball found Badri down the left-flank, who neatly lobbed the on-rushing Sandilands to allow Jouini to tap into an empty net in the penultimate minute of regulation time.
The result sees Esperance take control of Group B as they go top with eight points from four matches, while third-placed Horoya are set to face Zimbabwe's FC Platinum this evening.
Esperance XI: Jeridi, Derbali (Mbarki 90'+2), Dhaouadi, Yaacoubi, Ben Mohamed, Kom, Coulibaly, Badri, Chaalali (Rebai 81'), Belaiu, Khenissi (Jouini 73').
Pirates XI: Sandilands, Mbekile (Mahachi 79'), Jele, Ndengane, Maela, Motshwari, Mntambo (Shonga 63'), Mako (Gabuza 46'), Pule, Lorch, Mulenga.
Unused subs: Mabokgwane, Munetsi, Nyatama, Mlambo.