PAUL GASCOIGNE's sending-off in the 28th minute was the lowest point in a series of depressions for Rangers in Europe.
Having been similarly punished for dissent against Borussia Dortmund last season, the erratic midfielder this time aimed a kick at Winston Bogarde.
By the time Babangida rolled in the third goal - the net was empty after the heroic Snelders had pushed out a Ronald de Boer drive - the Scottish champions had also seen their captain Gough, as well as Cleland and Moore, cautioned.
All three will now miss the match against Ajax at lbrox on Wednesday week.
Durrant brought Rangers' only high point with his goal - a 10-yard shot - three minutes from the end, but there was still time for Wooter to score a fourth by lobbing Snelders.
Rangers had fallen a rather undeserved goal behind after 25 minutes and were just beginning to regroup when the England midfielder put them in deeper trouble.
Knocked to the ground by the powerful Bogarde, Gascoigne sprang to his feet and took a kick at the Dutch defender.
Gascoigne had been an integral part of the manager Walter Smith's adventurous plan, playing as an orthodox centre-forward with Laudrup and Albertz in support in a 4-3-3 formation that has been totally alien to Rangers in recent years. It was so unexpected that it was working.
indeed, the Englishman had made an outstanding early opportunity by dispossessing the lethargic Frank de Boer and running unchallenged towards Van der Sar's goal before uncharacteristically tripping over his own feet.
Laudrup missed what would prove to be a rare chance when a slack Ajax header compromised the goalkeeper, leaving him stranded as the Dane came in from the right. The Rangers winger, however, made an amateurish stab, sending the ball wide of the right-hand post.
Rangers' adopted style was working so fluently that they were able to scramble to protect Snelders whenever called upon, denying the Dutch the space they needed to inflict any damage.
Only a shoddy piece of play by Albertz allowed Dani to score the first of his goals. Taking the loose ball in plenty of space on his own 18-yard line, the German knocked it straight to Reuser.
The striker fed Babangida on the right and he produced a perfect centre which Dani from six yards, nodded low to the right of Snelders.
Ajax's advantage was doubled four minutes before the interval. Overmars, fed by Scholten, skipped past Moore on the left and delivered an impeccably weighted cross to Dani coming in from the right. This time the ball flew to the left of Snelders.
With Rangers by then in disarray, Ajax's Portuguese striker seemed to have secured his hat trick when a 20-yard shot sped past Snelders but crashed back off the underside of the bar.
If Gascoigne gave a passable impersonation of a striker while he was on the field, Snelders's impression of the man he replaced, the injured Goram, was flawless.
The Dutch goalkeeper made a string of saves which prevented a more serious defeat.
By the end the Ajax players were spending more time around Rangers' goal than they probably do with their wives.