Bouncing off an eight-game winless streak, Chippa desperately needed victory to avoid slumping further in a relegation contest, while Celtic aimed for third spot.
A brilliant save from Patrick Tignyemb denied Rhulani Manzini a third goal of the season from a well-directed header following a right-sided cross inside five minutes.
Celtic almost went in front with the help of Daniel Akpeyi nearly stuffing the ball from a corner by Kabelo Dlamini into his own net but the Nigerian managed to gather safely at the second attempt on 15 minutes.
Still, Chippa looked more threatening as Tercious Malepe crept up in unfamiliar territory to turn and get a shot away after nudging off a defender, but the final effort went wide midway through the half.
As the 30-minute mark went by, Tignyemb needed to rush off his line to prevent Manzini from pouncing on a poor back-pass by Tshepo Rikhotso, with Malepe dismal on the follow-up effort.
From a corner moments later, Mayambela saw his looping header crashing off the top of the crossbar on the back of poor defending as the hosts closed in on the breakthrough.
With two minutes to the break, Andile Mbenyane raced through on goal to get a low shot away but Tignyemb made his presence felt to stave the effort for a corner.
Brilliant work from Dlamini through the middle instigated a well-laid through ball over the top which Ndumiso Mabena ran onto to lob Akpeyi for the opening strike earlier in the second half for the visitors.
Livewire Thabo Rakhale was introduced to add liven up the home side’s attack, with Tebogo Makhobela making way a minute later.
For all their earlier dominance, the Chilli Boys were now on the ropes with the visitors appearing more and more promising on the ball whilst nearly adding a second with a low shot from Baloyi.
Akpeyi was being made to work as he needed to stop Mabena from bagging a second goal by getting down to prevent the effort from sneaking into the bottom corner closer to the final quarter.
Chippa closed in for the equaliser in the final minutes, but Celtic held on for the maximum points to move into third spot
Chippa: Akpeyi, Makobela, Macheke, Nsabiyumva, Modisane , Thlolane , Sangweni , Malepe , Mayambela , Mbenyane , Rhulani Manzini.
Subs: Komane , Mzimela , Rakhale , lentjies , Sali , Maphanga.
Celtic: Tigyemb, De Jongh, Rikhotso, Letlabika, Sam, Baloyi, Phalane, Masuku, Dlamini, Mangweni, Mabena.
Subs: Chaine, Potsane, Maema, Mabaso, Shikweni, Lingwati, Motshegwa.