With the relegation-threatened home side levelling the scores at 1-1 with just over 20 minutes remaining, it seemed as if they had done enough to secure a vital point from the match.
But a two-goal burst in just over 60 seconds took the game away from AmaZulu as Jeremy Brockie and Thuso Phala helped SuperSport surge ahead.
The three points means a jump to sixth for SuperSport from eighth with their tally of 38 points with two games left in their season.
For AmaZulu, the loss means they stay rooted to the bottom of the table on 24 points with two games remaining. Moroka Swallows remained three points ahead in 15th after their crucial 1-0 win over Maritzburg United on Friday.
Phala showed some individual skill in the 17th minute by dribbling two defenders and cross for an unmarked Brockie but his shot could not break the deadlock.
SuperSport took the lead in the 39th minute through a deft strike from Daine Klate. The former Pirates player stepped up to take a free kick just outside the box, and noticed a gap in the wall where he swiftly sent the ball through on its way into the back of the net to make it 1-0 to the visitors.
AmaZulu levelled the match in the 68th minute. From Sifiso Hlanti corner Sadate Ouro-Akoriko rose to meet the ball uncontested in the six yard area and slot home the equaliser to send the home crowd into wild celebrations.
AmaZulu gifted the visitors their second goal in the 79th minute as a harmless cross into the box was allowed to bounce, and a grateful Brockie obliged by deflecting the ball goalwards to make it 2-1 to SuperSport.
Phala made it 3-1 a minute later. Brockie this time made the run into the box drawing the attention of both defender and goalkeeper before laying the ball off for Phala in the middle who had no problem driving the ball home to seal the result for the Pretoria outfit.