Goals from Shaun Maloney, from the penalty spot, and Stephen McManus made the difference as Hibs played the last half-hour with ten men after goalkeeper Simon Brown was sent off.
Substitute goalkeeper Zibi Malkowski also saved a late penalty from Maloney as Celtic dominated the second half.
Hibs posed a threat from the start with the pace of Ivan Sproule a constant headache to the Celtic defence.
Chris Killen had the ball in the net after only six minutes but it was disallowed for offside.
Hibs took a deserved lead midway through the first half when Derek Riordan curled a 20-yard free-kick into the top corner of the net.
The Edinburgh side had chances to add to the lead. Kevin Thomson tested Artur Boruc with a long-range effort and then Stephen Glass dragged a shot wide with only the goalkeeper to beat.
But Celtic equalised nine minutes from the break when Maloney was pulled down in the penalty area by Steven Whittaker and he brushed himself down before firing home the spot-kick.
Celtic finished the half strongly and Simon Brown saved well from a well-struck shot from Roy Keane.
Gordon Strachan's side moved in front after an hour when Hibs failed to clear a corner and McManus scored from Maciej Zurawski's pass.
A minute later, Brown was red-carded for handling the ball outside the box to deny Zurawski a goalscoring opportunity.
Whittaker pulled down Maloney in the area again after 71 minutes and was fortunate to escape another booking but substitute goalkeeper Malkowski saved Maloney's penalty kick.
Ten-man Hibs finished strongly but could not unlock the Celtic defence.