Celtic made it a total whitewash of their Glasgow rivals thanks to a last-minute goal by Chris Sutton.
It was no more than the home side deserved after they had laid siege to the Rangers goal for almost the whole of the second half.
Sutton brilliantly held off some desperate challenges by Frank De Boer and Zurab Khizanishvili before skilfully curling his shot into the top corner from 20 yards, with keeper Stefan Klos absolutely helpless.
This is the first time in the post war era that either team has beaten its greatest rival in all four league fixtures and Celtic have the added bonus of a Scottish Cup victory as well.
It was impossible not to feel some sympathy for Klos as at times the keeper almost single-handedly denied Celtic with some good positioning and brave saves.
The match started off in controversy when in only the third minute Celtic were denied the opening goal.
Stan Varga diverted the ball home from Alan Thompson's free kick, only to have his goal disallowed for a Henrik Larsson foul off the ball.
Rangers forced a series of corners early on, without creating much danger, although a header from Alan Hutton drifted narrowly over.
Klos was called upon to make the first of many saves when he dived to his left to gather Larsson's free-kick at his post after De Boer had fouled Stephen Pearson.
Klos then did well to punch clear Larsson's looping header from almost under his crossbar when under pressure from the formidable Sutton.
After some good play by Mikel Arteta, Michael Mols' flick was deflected for another corner for the Ibrox side.
The visitors almost made one of these corners count when De Boer's near-post header from Arteta's corner was brilliantly turned away by keeper David Marshall.
Mols was then given space as Rangers enjoyed their best spell just before the interval. Marshall spilled the Dutch strikers fiercely struck shot and Steven Thompson should have done better than spoon the rebound high over.
Chris Burke cut in from the right before sending a superb cross along the six-yard line, but neither Thompson or Mols showed the desire or speed of thought to take a chance and go for it.
If the first half could be described as an even contest, then the second was anything but as Celtic dominated from start to finish.
The game became somewhat overheated with Bobo Balde booked for a foul on Mols with Fernando Ricksen and Arteta quickly following him into the referee's book.
Stilian Petrov watched his shot turned behind by Klos before Didier Agathe's pace allowed him to chase Steven Hughes as the Rangers player advanced into the box in a rare attack.
After a slip by Hutton, Larsson squared to Petrov whose shot ended up in the sidenetting with many Celtic fans convinced he had scored.
Agathe then ran almost the length of the park before his shot suffered the same fate as Petrov's.
After Khizanishvili fouled Sutton, Thompson's well struck free-kick was gathered at his post by the alert Klos.
Sutton then squandered a great chance when he was left unmarked from Neil Lennon's cross, but his header was too near Klos who managed to touch the ball over the bar.
Larsson then twice shot straight at Klos from half chances before Petrov was blocked by Khizanishvili and De Boer as he rode his way into the penalty box.
Celtic then passed up their best chance of the match and almost unbelievably it was Larsson who was the culprit.
Petrov could have shot himself, but elected to cut the ball back to Larsson who from no more than ten yards in front of goal sidefooted his shot tamely at Klos.
Despite all the pressure, Celtic almost suffered in the closing minutes the gravest of injustices. From a Paolo Vanoli cross, Thompson got his head to the ball before Marshall, but the Rangers striker was unable to direct his header on goal.
The home side's relief at that escape turned into absolute joy when Sutton controlled a long ball before shrugging off efforts to block him before shooting home superbly.
Celtic manager Martin O'Neill was gushing in his praise of Sutton after the match.
He said: "It was a wonder goal and no more than we deserved. Chris held off two challenges and shot home almost in the same movement and to beat Klos today was saying something.
"My players were well up for the game, but everything seemed to go straight at Klos. He's a top-class keeper but we were always looking for a goal even though time was not on our side.
"Our second-half pressure was top drawer and there was no doubt we were up for it and deserved the victory.
"I would agree it was pretty difficult to win over Rangers five times in the same season and there was motivation in this game for them as well as us." When questioned on the possibility of Rivaldo coming to Parkhead, O'Neill would not be drawn other than to say: "I'm sure another 15 clubs are also in for him, but when we came within a couple of minutes of making the last 16 of the Champions League this season, the best way to go that step further is to get the best players available, so who knows what might happen." Rangers manager Alex McLeish looked crestfallen after the match. He said: "I now know how Celtic felt last year. We gave everything. A lot of people had us as lambs to the slaughter this game as this was my weakest squad I've taken to Parkhead this season.
"We gave 100 per cent and my young players should take something from this.
"Everything came right back at us in the second half and yet again we've been beaten by a long ball through the middle and we didn't deal with the first or second ball." When questioned about Ricksen's reactions to Thompson after the goal, McLeish said: "Fernando alleges that Thompson slapped him at the goal and that it was a vicious slap." Certainly tempers were running high at the end with referee Hugh Dallas dispatching his assistant referee up the tunnel to ensure no further trouble.
Man of the Match: Neil Lennon - Yet again the fiery midfielder dominated the main action areas and drove his team on when it seemed that they would never score.