It was understandable that it was not a vintage performance by the home team after the superb efforts in midweek in winning against Benfica in the Champions League.
However, an own goal from Stephen Craigan and a second from the impressive Maciej Zurawski was enough to see the Parkhead club through against a spirited Motherwell side.
When Motherwell's Scott McDonald scored with just over ten minutes remaining there was some panic in the home ranks, but Celtic managed to close the game down without any further scares.
The home side made an early breakthrough when Shunsuke Nakamura threaded a superb pass through to Zurawski.
The Polish striker rounded the keeper but his shot towards the empty goal lacked power, yet somehow Craigan and Mark Reynolds managed to get in each other's way in attempting to clear with the ball appearing to be deflected over the line by the unlucky Craigan.
The visitors were showing a positive attitude and Richie Foran's deep cross found Steven McGarry unmarked at the back post but he headed wide.
Calum Elliot fired in a powerful shot from the edge of the box which Artur Boruc did well to touch over.
Shaun Maloney did force the ball home from close range just before half-time but he was adjudged to have brought it under control with his hand.
Nakamura also created Celtic's second midway through the second half with a pass which split open the Motherwell defence, allowing Zurawski to side-foot home.
However, If Celtic thought they could relax, they were rudely awaken when McDonald volleyed home from close range after Keith Lasley's clever cross had been headed back across goal by Reynolds.
But the experience of the home side came to the fore as they closed the game out to secure three more precious points.