Kenny Miller and substitute Aiden McGeady both had chances to win the game in the closing ten minutes as Celtic strained every muscle to claim their 12th league victory in a row, but Hibs will also feel they deserved to take more than a point.
Substitute Stephen Glass shot over with the last kick of the match and Jiri Jarosik was fortunate not to concede a late penalty for handball, but Hoops captain Neil Lennon was even luckier to escape a second yellow card at 2-0 after a head-to-head clash with Scott Brown.
Celtic had been showered with praise following their Champions League defeat of Manchester United, but Hibs showed them no respect in the opening minutes.
Abdessalam Benjelloun and Brown had already gone close by the time Ivan Sproule fired them ahead after 12 minutes. Defender Stephen McManus appeared to handle Benjelloun's flick, but Sproule played on and hammered a sweet half-volley high into the net.
Benjelloun held off towering defender Bobo Balde and then shot narrowly over, but that marked the end of Hibs' total domination as the Bhoys finished the first half strongly.
Hibs regrouped after the break and only a crucial interception by Balde prevented a second goal for Sproule.
Home skipper Kevin Thompson then took matters into his own hands, bursting through two tackles before stabbing the ball past keeper Artur Boruc just after the hour mark.
Celtic looked beaten and were lucky not to lose Lennon following his spat with Brown, but they were handed a lifeline with 20 minutes left when Miller set up Evander Sno for a simple close-range finish.
Four minutes later winger McGeady pulled the visitors level with a stunning low drive beyond Zbigniew Malkowski.