A goal in each half from Lucky Baloyi and Lehlohonolo Majoro handed Amakhosi a much-needed victory.
Chiefs dominated the first 45 minutes, controlling possession and looking threatening in attack, while Celtic seemed out of ideas in front of goal.
But despite their domination, Chiefs seemed more eager to pass the ball in the final third, with nobody wanting to take responsibity for the final shot on goal.
Lehlohonolo Majoro came close to breaking the deadlock inside 10 minutes, but his stinging shot from just inside the 18-yard box hit the side-netting.
Amakhosi continued to push, and it paid off just after the half-hour mark, when Baloyi scored what will surely be one of the goals of the season.
Baloyi let fly with a rocket of a shot from about 35 yards, and the ball sailed into the top left corner, giving Thabani Stemmer no chance.
Celtic tried to get back in the game, but were outplayed in midfield and lacked spark in the attack. However, they came close to levelling the score just after the break, but were denied by some excellent keeping from Itumeleng Khune.
The visitor's first corner of the match resulted in a goalmouth scramble, and Letladi Madubanya tried an overhead-kick from six yards out – but his acrobatic effort was superbly saved by Khune with his feet.
Celtic came into the game a bit after that, and Madubanya should have equalised, but with just the keeper to beat he fired wide.
Three minutes later Majoro doubled Chiefs' lead, after some good teamwork. Masango forced his way into the box on the right and sent in a good cross, finding Majoro unmarked four yards out. The striker made no mistake, side-footing the ball home to make it 2-0.
Promising second half substitute Ransford Osei wasted a great chance when, in a one-on-one situation, he fired straight at Khune.
The game became more open as Celtic pressed forward in search of a goal and Chiefs looked to hit on the counter, but in the end Amakhosi held onto their two-goal lead, which takes them to fourth on the table with a game in hand.