A single goal in the opening minutes from Stilian Petrov turned out to be enough to give Gordon Strachan's men all three points but goalkeeper Artur Boruc was called into action to stop Hibs from getting back into the game.
Celtic took the lead after five minutes when Shunsuke Nakamura caught Hibs on the hop after Ivan Sproule's wasted scoring opportunity, and found Petrov waiting in the Hibs area to fire home confidently.
The goal signalled the start of a long period of Celtic dominance but despite holding the majority of the possession the visitors couldn't extend their lead.
Hibs had a strong penalty claim at the end of the first half when Bobo Balde clashed with Sproule in the area, but their shouts were ignored by the referee.
Celtic could have doubled their lead at the start of the second half when Nakamura cracked a powerful free-kick off the post, but this time Hibs did not let Celtic take control of the match and the home side made several good chances.
Steven Whittaker shot wide while Michael Stewart produced an on-target effort which was well saved by Boruc.
Sproule and Paul Telfer were both lucky not to be sent off midway through the second half when they tangled following a tackle, but referee Craig Thompson showed great restraint in showing each player a yellow card.
Hibs kept the pressure on Celtic as they sought an equaliser, coming closest in the closing minutes when Whittaker forced a fine save from Boruc, who notched up his third successive clean sheet.