The Parkhead side had lost just one league game this season, which was back in August, to Hearts, but for all they have a commanding lead at the top of the table, they remain short on fluency and this will go down as another three points that Gordon Strachan's side ground out.
Hibs, might have appeared on John Collins' first return to Parkhead a little cautious with a 4-5-1 formation that was spearheaded by Steven Fletcher and had Scott Brown playing in an unfamiliar role behind the frontman.
However, for all that Celtic dominated the early stages, Hibs used their pace to great effect and looked capable of catching the Bhoys on the break on a couple of occasions.
Indeed, Celtic had Artur Boruc to thank for the fact they went into the break on level terms after the Pole denied Guillaume Beuzelin and then Sean Lynch, both with fingertip saves round the post.
To add further menace to Hibs' attack, Ivan Sproule was introduced after the break, but any hope the visitors had of frustrating their hosts was short-lived.
Nine minutes into the second period Aiden McGeady produced a moment of magic to open Hibs defence. The Irish international floated a perfect cross into the Hibs box and Beattie bulleted a header past Andrew McNeil.
To compound Hibs' misery Sproule did not see the end of the game. The Northern Irishman received a straight red card six minutes from time for a crude lunge on Lee Naylor with his studs showing.
There was further good news for Strachan, whose side not only went 22 points clear until Rangers play tomorrow, as he was also able to welcome back Mark Wilson who has not played since December.
Steven Pressley, Stephen McManus and Kenny Miller were also back in the starting line-up which should offer the Celtic manager confidence ahead of the forthcoming Champions League tie against AC Milan.