Mhango bagged a second-half brace to claim the spoils at Mbombela Stadium.
The win sees Celtic up to 10th place on the log with 20 points, while Aces dropped to eighth with 21 points.
Celtic offered very little in terms of attack in the first half and were completely outplayed by the home side.
Still, despite Aces controlling the possession stakes their decision making in the final third was poor and their shooting was woeful.
Clive Barker’s men fashioned their first chance on goal in the fourth minute when Tshidiso Tukane worked himself into space on the edge of the box, but shot inches wide of the goal.
Roughly 10 minutes later Aubrey Ngoma did everything right as he worked his way into the box after dribbling past a couple of defenders, but his shot bounced off the top of the crossbar.
Collins Mbesuma should have done much better in the 30th minute when he met a Tendai Ndoro cross, but his shot was a timid one and easily saved by the Celtic keeper.
Ndoro had an opportunity himself eight minutes later, but his finishing was poor as he fired wide from just inside the box.
The second half was a completely different affair and saw Celtic turn the tide.
In the 57th minute Mhango was at his best when he turned home a cross from Thapelo Morena to give the away side the lead.
Aces tried to fight back, but they struggled to break down a stubborn Celtic defence.
Celtic made sure of all three points in the final minute of the game when Mhango grabbed his second following a goalmouth scramble inside the Aces box.