The home side had fought from two goals down to take the lead at Peter Mokaba Stadium, but they were denied victory after a lapse of concentration at the back, and Gavin Hunt's men remain unbeaten in the League.
United started the better of the two sides, passing the ball around nicely, and Clifford Mulenga in particular was a real source of danger for the Leopards defence.
On 15th minutes Mulenga made his way into the box and produced a clinical finish, finding the bottom right corner of the goal with a well-placed shot.
Four minutes later SuperSport doubled their lead when Mulenga turned provider and supplied a great through ball for Mabhuti Khenyeza.
With just the goalkeeper to beat Khenyeza produced a powerful shot and added a second goal.
But Leopards were not to be outdone and fought their way back into the match.
Rodney Ramagalela pulled a goal back on half an hour, pouncing on a ball that had bounced off the woodwork after Raymond Monama had taken a shot.
At the start of the second half Mogezi Bobe provided a great pass across the face of goal and Brian Amidu was at the back post to drive the ball home.
Four minutes later Leopards took the lead, from a well worked set-piece.
Monama produced an in-swinging corner-kick, and Mabunda rose above the United defence to head the ball home emphatically to make it 3-2.
SuperSport tried to find their way back into the game and, just as all seemed lost, substitute Sameehg Doutie found an equaliser for the visitors in the dying seconds of the match.
A swift passing move found Doutie in space inside the box and he placed a shot beyond Omony to earn SuperSport a share of the spoils.