Celtic took control of the game early on and began to look threatening in attack.
In the ninth minute, James Forrest sent a dangerous ball across but Hibs managed to just about clear their lines.
Celtic then took the lead on 11 minutes when Paddy McCourt's cross was met by Mikael Lustig, 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. Victor Wanyama got a flick on Filip Twardzik's free-kick to send it goalwards, but Ben Williams just touched it behind.
The Hoops came close once again after 19 minutes when Forrest set up Gary Hooper, who hit an 18-yard shot onto the underside of the bar.
Forrest, who was giving the visitors' defence a torrid time, fizzed a shot just wide on 28 minutes.
Hibs had their first effort on goal after 37 minutes when Leigh Griffiths's overhead kick went over the bar from a tight angle.
Hooper hit the woodwork again on 40 minutes, heading an Adam Matthews cross onto the post.
The half-time whistle blew with a dominant Celtic side 1-0 up against Hibernian.