Celtic took control of the game from kick-off and threatened to grab themselves an early goal.
A dangerous ball from James Forrest nearly delivered that goal, but Hibs managed to clear their lines.
However, two minutes later, Celtic did take the lead through Mikael Lustig. Paddy McCourt's cross was met by the defender, who fired his shot into the back of the net to make it 1-0.
A minute later, the home side nearly had a second goal. Filip Twardzik's free-kick was flicked on by Victor Wanyama to send it goalwards, though Ben Williams just touched it behind.
On 19 minutes, The Bhoys came close once again when Forrest set up Gary Hooper, who fired an 18-yard shot onto the underside of the bar.
A Leigh Griffiths overhead kick gave Hibs their first effort on goal after 37 minutes, however, his effort went over the bar.
Hooper hit the woodwork again on 40 minutes, heading a cross from Adam Matthews onto the post.
The half-time whistle blew with a dominant Celtic side 1-0 up against Hibernian.
Hibs came out for the second half looking like a rejuvenated side and came close to a leveller on 47 minutes. Griffiths's free-kick was touched on by Eoin Doyle and smacked off the post.
The away side did get their equaliser after 53 minutes when a lack of communication between Lustig and Fraser Forster allowed Clancy in to make it 1-1.
Celtic went in search for another goal to restore their lead and on 67 minutes went 2-1 ahead. Twardzik's free-kick caused plenty of problems for Hibs as Lustig slid in before James McPake put the ball into the net.
Just six minutes later, Hibernian drew level for the second time, after Paul Cairney skipped past a challenge before firing a low shot into the net to make it 2-2.
Celtic came close to going back in front after 83 minutes, when Kris Commons's delivery fell to Twardzik, but he could only blaze over.
Neither side could find a late winner and the game ended in a 2-2 draw.