The Chilli Boys were dealt a massive blow when Rhulani Manzini was sent off in the first half whilst two goals in the second stanza for Musa Nyatama sealed the deal for the Free State side.
As expected Chippa controlled possession of the ball early on, although they proved not to be penetrative enough once their neat passing game saw them into attacking areas.
In what was one of the first real chances of the game Justice Chabalala was forced to slide in to clear after Daniel Akyeyi got a hand to Dumisani Zuma's shot and deflected it into the path of Atusaye Nyondo.
Chippa's gameplan was disrupted midway through the first-half when the focal point of their attack Manzini was shown a straight red card after an off the ball headbutt on Alfred Ndengane.
Despite a numerical disadvantage the Chilli Boys managed to retain control of the ball and hardly gave Celtic a sniff although they themselves were unable to create much going forward.
Moments after the half-time break a cross-cum-shot from Zuma forced Akpeyi to quickly readjust and tip the ball over the bar.
At the other end Paseka Mako got behind the defence and beat an on-rushing Patrick Tignyemb to the ball but from a difficult angle he failed to find the target with the outside of his boot.
In between the sticks for the away side Akpeyi continued to do a good job as he held onto shots from Vusi Shikweni and Lantshene Phalane.
Dan Malesela's men were being treated to some of their own medicine as Celtic capitalised on having an extra man and continued to boss the second half with the away side's goal constantly under seige.
Eventually the pressure paid off as a neat sequence of passing resulted in a chance for Nyatama to direct home untidily for the game's first goal.
At the other end Chippa almost hit back immediately through Andile Mbenyane who had only just come on for Menzi Masuku.
The game was put to bed in the dying moments of the match as diminutive trickster Kabelo Mahlasela was brought down in the box and Nyatama bagged his brace from the spot.