Stilian Petrov was the main home threat with a well taken hat-trick while Shaun Maloney and Shunsuke Nakamura contributed with further goals.
Manager Gordon Strachan wanted football with style and he certainly got that on the evidence of this performance.
This victory keep Celtic hot on the heels of Hearts who still lead the SPL by three points.
In the opening minutes Craig Beattie was too firm with his pass to Nakamura and the chance slipped by but it did not take long for Celtic to break through as Maloney hit a crisp pass through to Petrov who tucked the ball home from six yards.
It was a well worked goal and was quickly followed by another.
Petrov and Nakamura combined well before finding Beattie whose cross to the back post was slid home by Maloney.
Motherwell was stunned and fell further behind when Beattie laid the ball off to Petrov whose powerful shot from the edge of the box found the net via the post.
Celtic were content to knock the ball about after scoring three goals in 10 minutes but nearly paid the price when Dianbobo Balde was sloppy with a pass back but Richie Foran could not take advantage.
In the second half Nakamura added a fourth with a superb 25-yard free-kick into the top corner before Petrov finished the scoring and completed his first hat-trick with a low shot from Sutton's pass.