Both teams had chances but the two goalkeepers, Itumeleng Khune and Ronwen Williams, were on high alert to thwart any danger.
The match’s first real chance fell to Chiefs in the seventh minute when Tefu Mashamaite rose above the United defenders to head a Siphiwe Tshabalala corner, but his effort missed the target.
Sibusiso Khumalo played a long ball forward for United but Khune was quick off his line to clear the danger under pressure from Thuso Phala in the 16th minute.
Tshabalala came close to opening the scoring for Chiefs in the 22nd minute as he turned Thato Mokeke inside-out and pulled the trigger, but Williams was equal to the task.
Khumalo conceded a free kick in the 42nd minute but George Maluleka’s attempt at goal was gangly collected by Williams.
On the stroke of half-time, United striker Bradley Grobler watched in agony as his piledriver flew inches wide of Khune’s upright.
In the 49th minute, Edwin Gyimah came to United’s rescue as he made a timely challenge block to thwart Tshabalala’s cross into the box.
The visitors had a chance to take the lead in the 54th minute, but Mashamaite miscued his clearance and the ball fell kindly for Phala, who rifled the ball wide of the target.
Matsantsantsa came close again in the 58th minute, but this time Khumalo’s grass-cutter from a free kick on the edge of the box missed the target.
In the 73rd minute Lebese was hacked down by Thabo Moloi and Bernard Parker took the resultant free kick but Williams, at the top of his game, made a great stop.
In the 86th minute Lebese found himself unmarked inside the box but opted to round the goalkeeper instead of taking a shot but Williams scrambled the ball off the Chiefs player’s feet.
Lebese’s persistence finally paid off in the 90th minute as he buried a pass from Siboniso Gaxa to give Chiefs the lead.
Lebese was not done yet and came back to haunt United with another wonder goal in the 93rd minute to seal a semi-final place for Amakhosi.