But late goals from substitute Glenn Loovens and Scott Brown ensured Celtic remained top of the table.
The match was a good advert for the SPL with both sides looking to attack at every opportunity.
Derek Riordan, who failed to make the grade at Celtic, was out to prove a point and his powerful free-kick was well saved by Artur Boruc.
Brown chipped over from 25 yards before Scott McDonald pulled his shot narrowly wide.
Boruc produced a marvellous save from Riordan's shot after it had taken a wicked deflection.
Hibs squandered a great chance to take the lead when Steven Fletcher's reverse pass put Colin Nish through but the striker failed to control the ball and the chance was lost.
Celtic punished this miss by taking the lead shortly after.
Shunsuke Nakamura's corner was missed by John Rankin at the near post leaving Stephen McManus to turn his shot home from six yards.
The home team added to their lead when McDonald cleverly dummied a McManus pass and young striker Cillian Sheridan touched the ball around the Hibs keeper before coolly side-footing home.
Hibs were thrown a lifeline when Fletcher's snapshot was deflected by Nish past Boruc.
It looked even better for the visitors just after the break when Ian Murray's pass inside Barry Robson showed up the wing-back's lack of pace and Nish's cross was guided home by Fletcher.
Celtic responded with some sustained pressure on the Hibs goal with keeper Yves Makalamby twice saving the ball from McDonald.
The Aussie striker was lucky not to be sent off for a bad tackle on David van Zanten before Celtic restored their lead.
Shaun Maloney's corner was headed home by Loovens, before Brown rounded off a man of the match performance with a 20-yard strike into the bottom corner after a one-two with McDonald.