They gave their hosts a massive uphill task by scoring twice in the opening nine minutes. The first goal came from a close-range effort by Shaun Maloney, set up by Scott Brown's fifth-minute cross.
Four minutes later Georgios Samaras burst through the heart of a static Motherwell defence to drive a low shot past the helpless Graeme Smith.
Motherwell did steady the ship for the next 15 minutes, but another two-goal burst before the break looked to have put an end to any resistance.
On 24 minutes Scott McDonald gathered a thrown-in from the right and turned Mark Reynolds before firing high past Graeme Smith.
McDonald then combined with Samaras on 42 minutes to release the Greek striker who was once again clean through and left Graeme Smith with no chance.
Motherwell regrouped at the break and came out fighting and two early goals showed their resistance had not been broken.
Ten minutes after the restart a Stephen Hughes chip into the box was headed into the path of John Sutton by Keith Lasley and the English striker sent a sweet shot into the bottom left-hand corner of the net.
Two minutes later Hughes was once again the provider as he sent David Clarkson clean through the centre of the Celtic defence. The Scotland striker kept his cool to draw Artur Boruc and slide the ball under the advancing keeper.
It took a stunning save from the Celtic keeper to keep the home side at bay when, with ten minutes left, he threw himself full length to keep out Clarkson's near-post header.
In the end both sides will have taken something from the game as they look forward to their midweek travels.