Ben Malango and Zambian Rainford Kalaba scored to give the "Ravens" a two-goal lead 26 minutes into the Group D clash in southern Congolese mining hub Lubumbashi.
Mazembe applied continuous pressure in the closing stages with Malian centre-back Salif Coulibaly turned into a makeshift striker.
There was no way through a solid SuperSport defence, however, and Mazembe had to settle for a point and a share of the group lead with SuperSport and Horoya of Guinea.
The three clubs have five points from three matches with SuperSport first on goals scored and Mazembe second on goals difference.
Each match between them has been drawn and they all defeated the other club in the mini-league, Mounana of Gabon.
SuperSport joined a small group of teams to leave Lubumbashi with a point from a CAF fixture despite resting several regulars, including goal poacher Jeremy Brockie.
The 29-yeasr-old former New Zealand international is the leading scorer this season with seven goals in the Confederation Cup, the African equivalent of the Europa League.
Zesco United of Zambia became Group C leaders thanks to a 1-0 victory over Angolan visitors Recreativo Libolo in a match that ended with both teams reduced to 10 men.
DR Congo-born Idris Mbombo, one of several "imports" in a multi-national Zesco line-up, nodded the winner on 27 minutes when a defender failed to cut off a cross.
Angolan Celson Costa was red-carded during the second half in Ndola and Nigerian Anthony Akumu received a similar punishment after two yellow cards.
Smouha of Egypt and Al Hilal Obeid of Sudan drew 1-1 in Mediterranean city Alexandria in the same group, ending a four-match cycle of home victories in the mini-league.
Ahmed Hassan Mekki converted a softly-awarded Smouha penalty on 39 minutes after he appeared to slip in the box when tussling for possession.
Hilal equalised after 68 minutes when Egyptian Mahmoud Ezzat sliced an attempted clearance over goal Mohamed Abo-Gabal.
Zesco have six points after three rounds, Smouha and Hilal four and Libolo three with the group winners and runners-up qualifying for the quarter-finals.