The visitors carved out their first chance after 10 minutes but defender Clayton Daniels could only head straight at Ley Matampi at the far post.
SuperSport should have been ahead two minutes later as Thuso Phala picked out Bradley Grobler at the far post, but the striker fired wide with the goal at his mercy.
In the 18th minute, Mazembe took the lead against the run of the play courtesy of an error from Ronwen Williams, who failed to deal with Adama Traore's effort from 20-yards out, 1-0.
Eric Tinkler's charges took the game to the hosts for the rest of the second half, as the likes of Dove Wome and Grobler failed to take their chances.
Nevertheless, SuperSport went into the break trailing the Congolese outfit by the lone goal.
SuperSport started the second on fire and they leveled matters inside the first two minutes as Sipho Mbule rifled the ball past Matampi from 25-yards out, 1-1.
However, Mazembe restored their lead on 66 minutes as Daniel Nii Adjei caught the SuperSport defence napping and sent a fine header past Williams from a corner.
Tinkler responded by withdrawing Jeremy Brockie for Fagrie Lakay in the 72nd minute as SuperSport pushed for an equaliser.
Mazembe had a chance to seal the win in the 80th minute but Elia Meschak failed to make contact with an inviting cross with the goal at his mercy.
SuperSport were in need of an equaliser, but it was the hosts who dominated in the closing stages of the second half.
However, the home side failed to add their advantage as the score remained 2-1 in their favour at the full-time whistle.
Mazembe: Matampi, Issama, Kimwaki, Kabaso, Kasusula, Sinkala, Adjei (Mputu 81'), Kalaba, Ushindi, Malango, A.Traore.
Subs: Gbohouo, Zola, Mondeko, Kouame, Mputu, Asante, Elia.
SuperSport: Williams, Nhlapo, Daniels, Mashamaite, Modiba, Furman, Mbule, Phala, Wome (Kekana 78'), Brockie (Lakay 72'), Grobler (Farmer 84')
Subs: Pieterse, Farmer, Kekana, Lakay, Nkhatha, Dube.