The Glamour Boys, without injured pair Khama Billiat and Leonardo Castro, lacked in creative spark and the result extends their winless streak in the Premiership to five games, in contrast to their run to the final of Nedbank Cup which takes place against TS Galaxy on May 18.
It was Celtic who made the early running in Polokwane and they enjoyed several decent chances in the opening 15 minutes as Kabelo Dlamini twice went close from the edge of the box while Menzi Masku sent a headed effort over the bar.
Chiefs, meanwhile, were struggling to create much of an impact going forward and it was Phunya Sele Sele who took a deserved lead midway through the opening half, when veteran striker Ndumiso Mabena curled a well-taken free kick over the wall and into the net via the inside of the left hand upright.
There was no real response from AmaKhosi, and with the Free State side also not showing much ambition in attack, the best the two teams could offer before the interval were a couple of harmless long-range shots.
Looking for a response from his men after the restart, Chiefs coach Ernst Middendorp brought on Siphosakhe Ntiya-Ntiya and Arohasina Andriamirado in place of Lorenzo Gordinho and Philani Zulu; yet proceedings remained tight as Celtic maintained their discipline and focus to good effect.
The next chance was to fall the way of Celtic, when Dlamini’s 58th minute drive flashed across the goalmouth, and it was only in the 70th minute that Phunya Sele Sele keeper Patrick Tignyemb had to make his first save of the night when he comfortably kept out Dumisani Zuma’s effort.
With eight minutes to play the stage seemed set for Bernard Parker to rescue Chiefs, but as time seemingly stood still, his attempt to turn in a cross went agonisingly wide.
Celtic could have added to the scoreline if Neo Maema had been more clinical with three good opportunities on the break late on, although it also took a brave block from Tignyemb on Zuma in the dying moments of the game to secure the three points.
The victory takes Celtic to the eighth spot on the standings, one point behind seventh-placed Chiefs and two ahead of Highlands Park in ninth.