A fantastic last-minute strike by Chris Sutton handed Celtic their fifth win of the season over Rangers.
Rangers looked like holding on for a draw after a backs-to-the-wall performance in the second half.
But they reckoned without Sutton who held off the challenge of Frank de Boer before curling an effort from the edge of the box round Stefan Klos.
The result means Celtic completed a whitewash of wins over their rivals for the first time in over 30 years.
Celtic started on the offensive and they had the ball in the net after only three minutes.
Alan Thompson swung in a free kick from the right and Stan Varga guided the ball beyond Stefan Klos, only for referee Hugh Dallas to rule the effort out for an infringement by Henrik Larsson on Frank de Boer.
Rangers pushed forward looking to make their own mark on the early stages of the game and a neat passing move culminated in Fernando Ricksen having his shot deflected wide.
Larsson tested Klos with a 20-yard free kick after 15 minutes that the German dealt with comfortably, and the keeper was called into action a few minutes later to punch clear under intense pressure from Chris Sutton.
Stephen Hughes was unfortunate to see a goal-bound volley deflected over the bar by Stilian Petrov and eight minutes before half time the midfielder tried to curl a shot past David Marshall, but Bobo Balde's intervention sent it wide.
From the resultant corner, De Boer met Arteta's corner with a glancing header at the near post, but Marshall reacted superbly to push the ball away.
Michael Mols was next to test Marshall and though the keeper could not hold the Dutchman's swerving effort from the edge of the box, he was out sharply to close down Steven Thompson who could only lob the rebound over the bar.
Stan Varga keeps a close eye on Michael Mols
Rangers started the second half well without really threatening the Celtic goal as tempers began to fray slightly.
At the other end, Varga almost squeezed an Alan Thompson corner in at the far post after 56 minutes and then Klos turned a Petrov effort round the post.
Petrov came close again after 62 minutes when Larsson's shot-cum-cross fell to him at the back post, but the Bulgarian could only slam the ball into the side-netting.
Klos dealt comfortably with a Thompson free kick but he had to be on his toes to tip a Sutton header over the bar after the Englishman was left unmarked only six yards out.
The German's reflexes were tested to the full again moments later when first he punched a Larsson header off the line and then clutched a similar effort from the same player, with Celtic claiming the ball and keeper were behind the goal-line.
Larsson should have made the breakthrough with seven minutes remaining when Petrov found him unmarked 12 yards out, but the Swede tamely hit the ball straight at Klos.
Sutton also hit a shot straight at the keeper and then glanced a header a yard wide, before Stevie Thompson headed wide at the other end.
But then Sutton latched onto a long clearance by Marshall and collected the return pass from Larsson before beating Klos to send the home support into raptures.
Celtic: Marshall, Varga, Balde, McNamara, Agathe, Lennon,
Petrov, Pearson, Thompson, Larsson, Sutton.
Lambert, Mjallby, Beattie, McGeady.
Rangers: Klos, Hutton, Frank de Boer, Khizanishvili, Vanoli,
Burke, Ricksen, Arteta, Hughes, Mols, Thompson.
Ball, Ross, McCormack, Adam.
Referee: H Dallas