In a week in which Celtic faced off against Aberdeen at Hampden and Leipzig in the Champions League, it was at Rugby Park where they really had to work for the win.
Goals from Callum McGregor and Nicolas Kuhn gave them the points but not before Kilmarnock had made them sweat.
The hosts would have been aggrieved to go into the break trailing.
They had enjoyed the better of the chances with Marley Watkins clipping the outside of Kasper Schmeichel’s post while Kyle Vassell had an effort deflected over the bar by Austin Trusty that looked goalbound.
By contrast, Celtic had looked fairly lethargic in the final third with Daizen Maeda and Nicolas Kuhn kept quiet by Kilmarnock.
Idah had forced a save from Robby McCrorie but there had been little real threat from Celtic.
Then, join the cusp of the break, Callum McGregor’s cross seemed to elude everyone – although Idah looked to claim a touch – before ending up in the back of the net.
To their credit, Kilmarnock looked to sustain the same pressure in the second period. Schmeichel had to save after Brad Lyons had drilled in a low effort at the back post.
Kuhn ought to have doubled Celtic’s lead after Liam Scales’ long ball pick him out, After exchanging passes with Idah, his effort was tame as he fired into the arms of McCrorie.
It could have been costly with Killie almost levelling immediately afterwards with Schmeichel forced to deny Innes Cameron.
Kilmarnock got closer again when Schmeichel was forced to get down tp his left-hand side to push away a Matty Kennedy effort after the winger had nicked possession and darted into the Celtic box.
Kuhn enabled Celtic to breathe a little easier when he netted their second of the afternoon to relieve the pressure they had been under.
The winger got away from Robbie Deas before cutting inside of David Watson and curled the ball low into the far corner for his tenth goal of the season.
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