As well as ending that unenviable winless sequence, the victory also handed Rangers a vital three-point lead in the quest for the SPL with the final Old Firm match to come at Ibrox after the league split.
The Rangers players, led by unlikely hero and scorer of the first goal, Gregory Vignal swarmed to the visiting supporters following Mike McCurry’s blast of the final whistle.
The league is certainly not won yet but today’s massive win was a giant leap in the right direction.
A red, white and blue tickertape reception had greeted the Rangers side prior to kick off as McLeish chose to start with the same 11 that had demolished Hibs the previous week.
Celtic, as expected, handed a debut to Craig Bellamy who formed a two-pronged attack alongside John Hartson, with Chris Sutton dropping back into midfield.
Bellamy, closely shackled by Marvin Andrews throughout an absorbing contest, looked lively and eager to impress but was guilty of passing up Celtic’s most threatening chances of a towsy and evenly-matched first half.
Ronald Waterreus, on his Old Firm debut, was the man Bellamy seemingly couldn’t beat. After just five minutes the Welshman struck a shot into the midriff of the keeper and ten minutes on, after beating the offside trap, Bellamy again found the Dutch stopper in his way as he tried to curl an effort into the far corner.
Waterreus wasn’t required to act when the striker then found himself through on goal for a third time, Bellamy slashing a shot tamely into the side netting – the offside flag rendering the chance void in any case.
Earning his corn, the keeper then reacted swiftly to block a Hartson stab at goal from short range after the striker had latched on to a flick from Stilian Petrov.
That aside, Rangers looked relatively comfortable at the back, with Sotirios Kyrgiakos – another taking his Old Firm bow – towering over Hartson time and time again.
As an attacking force, however, the Light Blues were not as productive. A corner forced after just 15 seconds offered early hope but it was to prove something of a false dawn.
Too often Vignal was wasteful with possession while Nacho Novo, unsurprisingly, was unable to do much with the hopeful long balls that were too often hoisted in his direction.
The second half continued in the same vein and within five minutes Bobo Balde and Andrews had traded bookings for two clumsy and late challenges on Fernando Ricksen and Hartson respectively.
After their cautious approach in the first half, Rangers looked more adventurous after the break and a delicious through ball from Barry Ferguson sent Novo scampering free.
His cut-back was cleared to Vignal only for the Frenchman to send a wild shot well wide of target.
The Frenchman was looking for his first goal since his summer move from Liverpool but his moment in the spotlight was still to time.
Dado Prso, of course, has no such stage-fright in front of goal and after 56 minutes he called Douglas into action for the first time in the match.
A purposeful Thomas Buffel run created the opportunity for the Croatian and, after he stepped inside Neil Lennon, Douglas instinctively thrust up his hands to block Prso’s fiercely-struck drive.
After a quiet start to the second half, Celtic roared back with two great chances shortly after the hour mark.
Alan Hutton mis-timed a tackle on Hartson – the defender was booked – and when Thompson swung in the resultant free kick, Andrews managed to get in front of the Welsh striker to stop what would have been, almost certainly, a goal.
Minutes later and Hartson was threatening again, evading his markers to tee up a shot on goal from around 10 yards.
Just as in the first half, however, Waterreus was Rangers’ saviour with a fine block, showing that, even at 34, age has not diminished his lightning-quick reflexes.
While the Dutchman was excelling himself at one end, it would prove to be an afternoon to forget for his opposite number.
There seemed little danger for Douglas when, with 70 minutes played, Vignal launched a speculative bash at Celtic’s goal from around 25 yards.
To the amazement of the 59,041 crammed inside Celtic Park, the ball bounced in front of the hapless keeper, struck him on the arms and trundled into the net to hand Rangers something of a surprise lead.
After years of gut-wrenching misery at this venue, the joyous celebrations from the visiting players and fans alike was certainly understandable.
It would get even better eight minutes from time. Ricksen’s through ball was misjudged by Laursen allowing Novo a free run through and the man who turned down Celtic in the summer didn’t need a second invitation.
With pinpoint accuracy, the Spaniard lobbed Douglas before celebrating with gleeful abandon in front of the delirious Rangers fans.
It had been a long time in coming but the wait was finally over.
RANGERS (4-4-2): 25 Wattereus; 20 Hutton, 16 Kyrgiakos, 5 Andrews, 18 Ball (A Rae 74); 4 Buffel, 2 Ricksen, 6 Ferguson, 24 Vignal; 9 Prso, 10 Novo
Subs not used: McGregor, Malcolm, Namouchi, Thompson, Burke, Lovenkrands
Booked: Andrews (50), Hutton (64)
CELTIC (4-4-2): 20 Douglas; 4 McNamara (McGeady 76), 6 Balde, 23 Varga, 16 Laursen; 19 Petrov, 9 Sutton, 18 Lennon, 8 Thompson; 47 Bellamy, 10 Hartson
Subs not used: Marshall, Henchoz, Juninho, Lambert, Maloney, Wallace
Booked: Balde (48)
Man of the Match: Ronald Waterreus