Neil Lennon improved his chances of landing the Celtic job on a permanent basis after claiming victory in his first Old Firm derby in charge.
Lee Naylor opened the scoring for the Hoops before Kenny Miller levelled for Rangers.
Marc Antoine Fortune restored the advantage on the stroke of half-time with what proved to be the winner before Lee McCulloch was red carded in the last minute for a challenge on Aiden McGeady.
Lennon admitted he wants the job on a permanent basis, while still on a high after the victory.
He said: “I don't know, it's up to the powers that be. I feel I've done enough.”
Celtic were effectively ruled out of the title race after they lost 4-0 to St Mirren in Mowbray’s last game in charge and then lost in the Scottish Cup semi-final to Ross County, but victories over Rangers are worth a lot to fans and the Hoops faithful could play a part in Lennon being appointed permanently.
Lennon praised his players for their commitment.
“I thought the team were magnificent. Overall they were magnificent tonight. It's not fair to single people out, it was a great team effort,” he said.
Goalscorer Naylor said of Lennon: “He's put me straight back in the team and he knows what I can do. I hope he gets the job because he's done a terrific job.”
Rangers finished the game with 10 men after Lee McCulloch was sent-off in injury time.
Lennon made five changes with Mark Wilson 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 McGeady and his low shot was helped into the bottom corner by a deflection off the unfortunate David Weir.
Rangers could have hit back but Miller's cross from the left was stabbed wide of the post by Lafferty.
Rangers levelled the match 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 and into the net to send the Bhoys fans into raptures.
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.
The substitute did well to prevent Miller grabbing a second when he raced off his line to block after the striker was set up by Lafferty.
A Naylor corner was nodded on by Keane for Kamara but he headed inches over. 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.
Celtic: Boruc, Hinkel, Wilson, O'Dea, Naylor, McGeady, Brown, N'Guemo, Kamara, Keane, Fortune. Subs: Zaluska, Samaras, Crosas, Ki, Rasmussen, Braafheid, Thompson.
Rangers: McGregor, Whittaker, Weir, McCulloch, Smith, Davis, Edu, Thomson, Naismith, Lafferty, Miller. Subs: Alexander, Boyd, Novo, Broadfoot, Fleck, Little, Stirling.
Referee: C Murray (Scotland).