Forward Mbwana Samata scored the only goal of the game in the 62nd minute as the Congo DR Super Ligue champions bounced back from a 1-0 defeat to Al Hilal last weekend.
The fixture passed off peacefully following the tragic events that occurred when the sides met two weeks ago for a domestic game. On that occasion, 15 people were killed following a stampede.
Mazembe stay bottom of Group A, but only on goals scored with all four teams now boasting three points from two matches.
ES Tunis suffered a 3-2 defeat to Al Ahli Benghazi on Saturday and have opted to sack manager Ruud Krol following their winless start to the tournament.
Sebastien Desabre, who took up the role of technical director in January upon Krol's appointment, will return to the dugout to take charge of first-team affairs.
Tunis are bottom of Group B, which is headed by Tunisian rivals CS Sfaxien.
The latter could only manage a 1-1 draw at ES Setif of Algeria in Sunday's other game.
Midfielder El Hedi Belameiri gave the hosts the lead after 12 minutes, but defender Ali Maaloul equalised for Sfaxien in first-half injury time to keep them ahead of Setif on goal difference.
