Kris Commons, who shrugged off a nasty ankle injury to make the game, drove the home side into the lead in the 14th minute and then grabbed a poacher's second the 51st minute before defender Mikael Lustig grabbed the third just after the hour mark.
Given that the home side could have wrapped up the title, Celtic Park was surprisingly far from full and in the fifth minute the home fans collectively held their breath as Leigh Griffiths' inviting ball from a free-kick was missed by everyone before skipping past Fraser Forster's far post.
But Hibs were unable to stretch their unbeaten run against the league leaders to three games and fell behind to Commons' strike. Gary Hooper took a pass from Charlie Mulgrew and laid the ball off to Commons who shrugged off the attention of Hanlon inside the box to drill the ball low past Williams and into the corner of the net.
Anthony Stokes had a decent chance three minutes into the second-half after Victor Wanyama played in Joe Ledley, whose cross was dummied perfectly for the former Hibs player but he failed to catch his shot properly and the ball bounced through to Williams.
Three minutes later Commons made it two. Wanyama played the ball to the supporting Lustig and when his cut-back found the former Derby and Nottingham Forest player he turned smartly from seven yards out and knocked it low past Williams.
It looked like it was a matter of how many the home side would score and in the 61st minute Lustig made it 3-0 from Ledley's cross. The Hibs players claimed the ball came off his arm on the way through but the strike stood.
From that point it became party time for the home fans as they listened for news from Motherwell and when word that St Mirren had come from one behind to go 2-1 up, the decibel levels increased.
But a late equaliser at Fir Park ensured the title race, if it can be called that, will go on.