Celtic manager Gordon Strachan's first taste of Old Firm action ended in misery as Rangers eased to victory and the visitors had two men sent off.
Alan Thompson saw red for a rash challenge before Dado Prso volleyed Rangers in front and Thomas Buffel added a neat goal after the interval.
Both sides were given late penalties, with Shaun Maloney scoring for Celtic and Nacho Novo on target for Rangers.
Neil Lennon was dismissed at the final whistle for arguing with the referee.
It was a comfortable victory for the champions, made all the easier by Thompson's folly - his third dismissal at Ibrox.
Celtic skipper Lennon angrily confronted Stuart Dougal after the match and he too was shown a red card.
The first 20 minutes were abysmal, with the ball pin-balling around the pitch at a frantic rate of knots and neither side capable of putting together a sequence of passes.
Celtic youngster Craig Beattie, preferred to Maciej Zurawski up front, had a glimpse of goal from close range but failed to connect with a wild swing as he was crowded out by Jose-Karl Pierre-Fanfan.
The game was littered with fouls and full-blooded challenges and Thompson's badly timed lunge at Novo saw the midfielder sent off after 23 minutes.
Novo then stole through the middle of the Celtic defence but goalkeeper Artur Boruc managed to push away the striker's unconvincing shot. The 10-man visitors then passed up a glorious opportunity to take the lead when Balde made a mess of a free header just six yards from goal.
The big defender was left unmarked from Stilian Petrov's corner but sent the ball crashing into the turf and it bounced high over the crossbar.
Celtic were looking the more organised despite their numerical disadvantage but soon found themselves a goal down.
Thompson was sent off early in the game
Marvin Andrews lumped a long ball into the penalty area and Prso met it on the volley to leave Boruc with no chance.
Celtic's Shunsuke Nakamura narrowly missed the target with a swerving 30-yard free-kick and Rangers skipper Barry Ferguson dragged a shot wide as the first half drew to a close.
Five minutes after the restart Rangers were further ahead thanks to a fine goal from Buffel.
The Belgian broke away from two challenges and managed to steer a low shot under Boruc from 16 yards.
Lovenkrands mis-hit wide from a promising position as more gaps appeared in the Celtic defence.
The same player later missed with an angled shot and then had an effort blocked by a great Mo Camara tackle.
The visitors were handed a lifeline in the closing stages when Ian Murray upended Maloney and the Celtic player got up to tuck away the penalty.
But, a minute later, Rangers won a spot-kick when Prso was manhandled and Novo shot home.
Rangers: Waterreus, Pierre-Fanfan (Malcolm 72), Andrews, Rodriguez, Ball, Alex Rae (Lovenkrands 45), Ferguson, Murray, Buffel, Novo, Prso. Subs Not Used: Klos, Thompson, McLean, Adam, McCormack. Booked: Rodriguez, Murray, Malcolm. Goals: Prso 34, Buffel 51, Novo 88 pen. Celtic: Boruc, Telfer, Balde, McManus, Camara (Virgo 87), Petrov, Lennon, Thompson, Nakamura (Maloney 54), Beattie, Hartson (Zurawski 67). Subs Not Used: Marshall, Aliadiere, Wallace, Lawson.
Sent Off: Thompson (23). Booked: Hartson, Lennon. Goal: Maloney 86 pen.
Ref: S Dougal