Kenny Miller scored twice on his return to Celtic Park and the excellent Pedro Mendes put his hallmark on the game with a third goal that will live long in the memory.
Daniel Cousin was also on the scoresheet for Rangers in what could be his last game for the club.
Cousin was sent off 15 minutes from time for two bookings and Celtic substitute Jan Vennegoor of Hesselink followed him a minute later for violent conduct.
Rangers showed their hand first and Cousin sent a header into the side-netting from a Steven Davis corner.
Celtic were quick to respond and came close themselves when Stephen McManus managed to get his head to a Shunsuke Nakamura free-kick but could not make clean contact and the ball drifted wide.
It was a pulsating start and Miller also had a look at goal for Rangers but sent his header high and wide.
Georgios Samaras had Celtic's first attempt on target after he met a Nakamura cross with his head but Allan McGregor made a comfortable save.
Aiden McGeady then tried his luck with a crisply-struck 30 yard shot which skidded narrowly wide as Celtic enjoyed a spell in the ascendancy.
McGregor made a reaction save to keep out a header from his defender David Weir under pressure from Shaun Maloney after an Andreas Hinkel cross had caused confusion.
But it was Rangers who took the lead eight minutes from half-time. Cousin beat Mark Wilson for pace and then defeated Artur Boruc with a shot low inside his near post.
Celtic responded within two minutes. Sasa Papac failed to deal with McGeady's cross and the ball broke to Samaras, who reacted swiftly to fire past McGregor.
The second half followed a similar pattern with chances early on for both sides. Charlie Adam squandered a free-kick from a good position and Maloney then curled a shot inches wide of McGregor's post.
But Miller then stunned Celtic Park when he put Rangers back in front. Kevin Thomson crossed for the striker to steer a controlled volley past Boruc from the angle of the six-yard box.
Mendes then struck a memorable Old Firm goal as Celtic failed to close him down at a corner and he cracked a thunderous shot beyond Boruc from fully 30 yards.
The game then boiled over when Cousin picked up his second booking for a foul on McManus and then Vennegoor of Hesselink was shown a straight red card for lashing out at Kirk Broadfoot just four minutes after coming on.
Boruc then spilled a cross from Broadfoot 11 minutes from time to present Miller with an easy fourth goal.
Nakamura pulled a goal back for Celtic in injury-time direct from a 25-yard free-kick.