Anthony Stokes, who returned from injury to partner Leigh Griffiths in attack, teed up first-half goals for Virgil van Dijk and Griffiths before Mikael Lustig’s late brace capped an utterly dominant display from the home side.
Stokes threatened with an early free-kick before Kris Commons, making his third successive start, saw his shot deflected over the bar as the home side pressed relentlessly.
They could not break down the massed ranks of the visiting defence, however, until the 26th minute when Stokes delivered a cross to the far post and Van Dijk rose to plant his header past Dan Twardzik.
Stephen Pearson was back in the Motherwell ranks after signing a short-term contract and the former Scotland international saw his cross-shot drift beyond the far post with Craig Gordon scrambling.
It was a rare foray out of their own half for the visitors and they duly fell further behind when Stokes picked out Griffiths who stole in to head past Twardzik (42).
Scott Brown was the next to threaten for the hosts but he could not keep his 10-yard volley on target and substitute Dominic Thomas finally sparked some life into Motherwell’s play, his left-foot drive hitting the side-netting.
Stefan Johansen then met Emilio Izaguirre’s cross but saw his header come back off the post and moments later Griffiths teed up Izaguirre who smashed the ball off the crossbar from five yards.
But it was to be only a temporary reprieve for Motherwell as substitute James Forrest played in fellow replacement Lustig (76) to sweep in the third goal and the Swedish full-back then produced the goal of the night as he rounded off a flowing move, meeting Griffiths’ cross with a fine diving header (81).
There was still time for Lustig to become the third Celtic player to hit the goalframe as the crossbar denied him an unlikely hat-trick after he had been set up by the unselfish Commons.