Indeed, Hibs had the better of the first-half exchanges, but Celtic stepped up the pace after the break where they were inspired by the excellent Scott Brown.
Lee Naylor hit a stunning solo opener and substitute Georgios Samaras scored with his first touch to keep the Hoops hard on Rangers' heels.
Hibs came charging out of the blocks and looked the hungrier of the two sides.
Steven Fletcher's well-weighted pass sent John Rankin racing through on goal, but Artur Boruc did brilliantly to spread himself and block from the midfielder.
But from the resulting corner, Ian Murray's powerful header broke to Thierry Gathuessi and his mis-hit shot was cleared off the line by Naylor.
Hibs had the ball in the net after eight minutes but Colin Nish was offside as he glanced in Rankin's cross.
However, the home side were impressive and Fletcher should have done better than fire over the bar with a clear sight of goal from 20 yards.
Inevitably, Celtic came back into the game and Jan Vennegoor of Hesselink hit the side-netting with a header from Shunsuke Nakamura's cross.
And Scott McDonald was screaming for a penalty after a clumsy challenge by Abderraouf Zarabi, but referee Kenny Clark wasn't interested.
Although McDonald was starved of quality ball, he looked dangerous and it took a great tackle from Hibs skipper Chris Hogg to deny the little striker.
But it was Hibs who came closest before the interval as Martin Canning put in a tremendous leap to glance Brian Kerr's corner inches wide.
However, it was a different Celtic after the break as they upped the tempo.
Brown was foiled by Canning's block and Aiden McGeady looked more in the mood as he cut inside to fire over the bar.
Brown was playing in a more advanced role and relished the chance to break forward.
The midfielder almost scored when he out-paced Zarabi, but Andrew McNeil did well to save at his near post.
But you could sense a goal was coming and it was a great solo effort from Naylor that broke the deadlock after 64 minutes.
He burst forward from halfway, got the brake off the ball off Ross Chisholm and finished coolly from 15 yards.
And Hibs' valiant challenge was over after 75 minuites when substitute Samaras scored with his first touch of the ball.
McGeady swung over a cross from the left and Samaras was unmarked to nod home off the post.
It was an easy job for Celtic to soak up Hibs' pressure and round off a good afternoon's work.