Motherwell at least showed more grit than most sides who visit Parkhead but the Fir Park side was eventually overwhelmed in the second half, though at least had the consolation of a late goal from Dirk Lehmann.
Goals from Henrik Larsson and Joos Valgaeren as well as an own goal from Scott Leitch were a fair reflection of Celtic's superiority, though this was a fairly subdued performance by the home side after their European exploits.
They should have taken an early lead when David Fernandez was hauled down from behind by Derek Adams, but Larsson unusually shot wide from the penalty spot.
Motherwell elected to play Lehmann against John Hartson to try and combat his height advantage, but the Celtic striker was just off target with just a header and Alan Thompson also saw his header graze the bar before FernandezÂ’ neat flick just failed to reach Larsson.
The home crowd became even more restless when keeper Rab Douglas had to pull off three brilliant saves in the space of a couple of minutes, twice from Ferguson efforts before stopping a curling header low on goal.
Celtic came out fired up for the second half, but when Hartson's header from a Fernandez cross eluded the Motherwell keeper, Leitch cleared off the line before Thompson following up shot wildly over.
The Celtic breakthrough was not long delayed when Larsson finished off Steve GuppyÂ’s cross, though the striker appeared to mis-hit his shot.
Then Larsson squandered another chance after rounding the keeper before Motherwell nearly equalised. Jamie McFadden beat two men in a run from the half way line before shooting narrowly past.
Celtic increased their lead with another fortunate goal, Steve Crainey's pass released Guppy and his cross shot was deflected in by Leitch.
Valgaeren notched the third to ensure the points for the home team when he forced the ball home from close range after the Motherwell keeper could only parry Hartson's header.
Lehmann reduced the deficit with a curling header, but when youngster Shaun Fagen was sent off for a second bookable offence, there was no way back for the Well