Ghanaian striker Mark Amofah netted either side of the half to send his team up to third place.
Both teams played at a steady pace in the blazing heat and produced a few scoring chances but no one was able to convert.
Celtic coach Khabo Zondo was forced to make two changes before the break as Ntokozo Sikhakane and Timothy Batabaire came off second best in 50/50 challenges. They were replaced by Grant Smit and Cyrille Mubiala in the 26th and 34th minutes respectively.
The visitors' diminutive midfielder Kleinbooi Taaibos worked endlessly in attack and defence and showed great vision too to set-up Amofah for a goal on the stroke of halftime.
Taaibos intercepted a pass and sped towards goal with four of his players supporting him. He chose the Ghanaian on the far left who just had to touch the ball to find the back of the net.
Cosmos pressured Celtic from the restart but were unable to breakthrough the impenetrable rearguard marshaled by Captain Gary Goldstone.
Amofah struck against the run of play with a speculative shot that caught Cosmos keeper Avril Phali offguard as it flew into the roof of the net.