Lee Naylor opened the scoring for the Hoops before Kenny Miller levelled for Rangers.
Fortune restored the advantage before the break with what proved to be the winner before Lee McCulloch saw red in the last minute.
Neil Lennon made five changes for his first Old Firm derby as Celtic interim boss.
Mark Wilson appeared to be preferred to Josh Thompson in the heart of defence after Glenn Loovens failed to recover from injury.
Robbie Keane, Landry NGuemo, Lee Naylor and Diomansy Kamara were also drafted into the side for the visit of Rangers.
The Scottish champions had a more familiar look after the weekend with Allan McGregor back in goal and Miller,
McCulloch, Steven Whittaker, Kyle Lafferty and Steven Davis also starting.
Rangers were dealt a blow early on when McGregor was injured while defending a Naylor corner and left the pitch on a stretcher after five minutes.
Unfortunately for replacement keeper Neil Alexander, his first task was to pick the ball out of the net when Celtic took the lead three minutes later.
Naylor stepped up for the free-kick after a Steven Naismith foul on Aiden McGeady and his low shot was helped into the bottom corner by a deflection off David Weir.
Rangers could have hit back but Miller's cross from the left was stabbed wide by Lafferty.
The game was becoming increasingly fiery and Kevin Thompson picked up the first yellow card before being followed into the book by McCulloch.
Celtic were dominating and had the chance to pile on the pressure again with another free-kick but this time Alexander was able to gather Naylor's shot.
But Rangers pulled a goal back three minutes from the break when Miller threw himself in front of a Whittaker cross and nodded past Artur Boruc.
Celtic were back in front on the stroke of half-time when Fortune met Naylor's cross and Alexander allowed the header to slip through his hands.
Rangers could have been back on level terms again when Miller cut inside from the left but he dragged his shot wide with Whittaker just a yard too slow to connect and prod home.
Then, with 53 minutes gone, Celtic were also forced to change goalkeepers.
Boruc had picked up a hand injury late in the first half which appeared to be causing a problem and he was replaced by Lukasz Zaluska.
He did well to prevent Miller grabbing a second when he raced off his line to block after the striker was set up by Lafferty.
Rangers were more dangerous now and Miller should have done better when he pounced on a Maurice Edu ball only to see his shot fizz past the post.
The striker was then perfectly placed to rifle home at the back post but a wonderful block from Wilson prevented Naismith's pass reaching Miller.
At other end, a Naylor corner was nodded on by Keane for Kamara but he headed inches over from a few yards out.
Zaluska then came to the rescue again with a great save to deny Davis, before Miller's shot crashed off the post.
The match ended in controversy when McCulloch was dismissed in the final minute for a second yellow for a foul on McGeady.