Kris Commons almost put the Hoops in front early on as his rasping 25-yard drive was inches away from nestling in the top corner.
Moments later, they fell behind after a poor backpass fell to Heffernan, who hit his shot through keeper Fraser Forster to score.
However, Celtic had a number of chances to equalise with Commons putting his shot over the bar.
The best opportunity of the half fell to Teemu Pukki who rounded the oncoming Williams, and seemed destined to slot the ball into the net only for Ryan McGivern's goal line clearance to keep Hibs in front.
Despite Celtic trying to find a way back into the game, their equaliser didn't come until late in the game thanks to substitute James Forrest, whose run and curling finish was too good for Hibernian's rearguard.
In the end, the draw keeps Celtic top of the league while Hibernian are in fourth place, eight points behind the Hoops.