An 11-match unbeaten run by United in the second-tier African club competition appeared in jeopardy after they wasted chances and trailed to a Saber Khalifa goal off a penalty.
Khalifa sent goalkeeper Ronwen Williams the wrong way with his penalty after 21 minutes at Lucas "Masterpieces" Moripe Stadium.
The spot-kick was awarded after an attempted clearance by SuperSport captain Dean Furman struck team-mate Morgan Gould on the chest and then the arm.
SuperSport had sufficient chances to have built a lead ahead of the return match in Tunisia on a date to be decided during the weekend of October 20-22.
The miss of the match came after only three minutes when unmarked Bradley Grobler sidefooted over the bar from just a couple of metres.
Confederation Cup leading scorer Jeremy Brockie, a New Zealander who has netted nine times, gave another disappointing display and was replaced during the second half.
Title-holders TP Mazembe of the Democratic Republic of Congo edged 2010 winners FUS Rabat of Morocco 1-0 in Lubumbashi through an early Ben Malango goal.
Malango notched his sixth CAF goal this season after only 14 minutes to inflict a fifth consecutive away defeat on the Rabat outfit in Africa.