The Bhoys started like a house on fire and took the lead after only three minutes when John Hartson converted Chris Sutton's left wing cross with a simple far post finish.
Celtic were lucky to have their lead at the break, and owe keeper Robert Douglas a huge pat on the back for a superb penalty save from Derek Adams.
The home side were handed the chance to level matters from the spot after the referee adjudged Johan Mjallby to have brought down David Clarkson.
Despite a spirited fight-back from Terry Butcher's side, Alan Thompson put the seal on the game with a superb free-kick after 71 minutes to clinch the points.
Hibernian were brought back down to earth after this CIS Cup win over Celtic on Thursday when they suffered a 2-1 defeat to Dunfermline at Easter Road.
Craig Brewster's first half strikes (1, 36) were enough to maintain their recent run of good form.
Derek Riordan did pull one back shortly after the hour mark, but it proved nothing more than a consolation.
Click below for match summaries:
Hibernian 1-2 Dunfermline
Motherwell 0-2 Celtic
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