To make matters worse for Neil Lennon's side, they are a man light after Cha Du-Ri was handed a straight red card for a foul on Lee Wallace.
Hosting Rangers started the better of the two sides and broke the deadlock in the 11th minute. Former Aberdeen winger Sone Aluko collected possession inside the Celtic half, before weaving his way into the area and slotting the ball underneath advancing goalkeeper Fraser Forster.
Celtic's response was positive and they almost levelled just one minute later. Georgios Samaras's strike from close range was parried by Allan McGregor, while Anthony Stokes's bouncing effort from the rebound struck the bar.
Stokes had another chance in the 25th minute, but McGregor was on hand to push the striker's volley out for a corner.
The away side were reduced to ten men in the 29th minute when Cha hauled down Wallace, who was through on goal, 20 yards from goal. Cha's dismissal was the 17th in the last 21 Old Firm derby matches.
Rangers made their numerical advantage count in terms of the possession thereafter, but they were unable to add a second goal.