Lehlohonolo Majoro scored early on for the visitors but, in the seventh and final minute of time added on, Mandaza looped a header over the diving Itumeleng Khune for a share of the spoils.
Chiefs though, only have themselves to blame after squandering numerous scoring opportunities throughout the match.
Amakhosi certainly didn’t start brightly as they struggled to get hold of the ball, but as they found their feet Stuart Baxter’s men began stringing passes together and creating chances on goal.
And one of these chances were finally converted when Reneilwe Letsholonyane headed down to Majoro, who duly obliged with a deadly finish to give his side the lead.
Chiefs continued to pile on the pressure with numerous corner-kicks and forays forward, but they were unable to find that final pass or cross that would lead to their second goal.
Majoro should really have doubled Chiefs’ lead two minutes into the second half when he found himself through on goal again, but this time he fired wide from about 14 yards out.
Shu-Aib Walters then kept his side in the game with two fantastic save within eight minutes. First, in the 60th minute, he produced a great reflex save to deny Majoro and then in the 68th he flung himself across the face of goal to tip a Bernard Parker shot around the post.
As the second half progressed Chiefs began to tire and United began to find some openings, the most costly for the visitors coming in the seventh minute of injury time.
Mandaza got onto the end of a Peter Petersen cross to level matters with virtually the last touch of the game.