Kris Commons, the hat-trick hero in the hammering of Hearts last Sunday, bagged a brace as the work-rate and slick movement so evident at Tynecastle was again given full rein by the champions.
Celtic, who had lost on both their last league visits to Lanarkshire, made a bright start under the Friday night lights.
Mikael Lustig forced a great save from Gunnar Nielsen as many fans were still making their way to their seats and Anthony Stokes worked the Motherwell keeper with a 20-yard free-kick shortly after.
Celtic appealed unsuccessfully for a penalty as Scott Brown's cross was blocked by Stevie Hammell while Lustig was again threatening when he headed over the top.
Motherwell were coming back into it with John Sutton and Stevie Hammell to the fore before Celtic landed a sucker punch, Commons (44) - played onside by a grounded Stephen McManus - doing the damage with a clever backheel from Stokes low cross.
John Sutton's header from a free-kick landed on the roof of the net and moments later the hosts fell further behind, Efe Ambrose (54) thumping home a header from Charlie Mulgrew's corner.
Scott Brown shot straight down the throat of Nielsen before Teemu Pukki was harshly booked for diving when he seemed to be caught by Adam Cummins in the box.
The rain that had been falling for much of the match turned to snow in the final quarter but there was to be no respite for Stuart McCall's bedraggled troops as Commons bagged his second goal of the night.
Emilio Izaguirre, popping up on the right, saw his shot parried by Nielsen and Commons tapped in (76) before Mulgrew and Pukki combined to tee up Stokes (78) at the back post for a classy fourth.
There was still time for substitute Bahrudin Atajic (90) to get in on the act, lobbing number five before referee Steven McLean put the hapless hosts out of their misery.
The only black spots on the night were when a flare was lit in the Celtic end before kick-off and a green smoke bomb was thrown on the pitch after the first goal.