Liverpool staged the most magnificent recovery of their 21-year European history at a near-hysterical Anfield.
Mark Walters' 83rd minute strike enabled Liverpool's patched-up team to achieve a feat that had been beyond all their illustrious predecessors.
Never before had any Liverpool side overturned a two-goal first-leg lead in European combat.
But the Kop saluted their heroes with a rousing chorus of "You'll Never Walk Alone" as Liverpool warned the rest of Europe that they are still a force to be reckoned with.
The Reds had the breaks but they were richly deserved by players who were keen to atone for their abysmal first-leg display.
Auxerre lost Hungarian international striker Kalman Kovacs through injury after 16 minutes and defender Frederic Darras sent off in the 75th minute for a second bookable offence - a foul on Walters.
But Liverpool made a dream start with Jan Molby slotting in a fourth minute penalty after Stephane Mahe tripped Steve McManaman.
Auxerre should have equalised five minutes later when Jean-Marc Ferreri sped down the right and crossed for the unmarked Kovacs.
But his stab for goal was blocked by the diving Bruce Grobbelaar.
The Zimbabwean had kept the score down in France and was to rescue Liverpool again after the break when he stuck out a leg to foil an Alain Roche volley.
Souness omitted Glenn Hysen and Dean Saunders, moving Mike Marsh to an unfamiliar right-back role. But Marsh was one of the outstanding players in a performance full of spirit. He mastered lively winger Pascal Vahirua and stole forward for the 30th minute goal which levelled the aggregate scores heading in a Houghton cross.
Goalkeeper Bruno Martini tipped around a swerving Molby free-kick before the first-half ended on a farcical note.
Two supporters were involved in a skirmish with stewards and police in the back of the French goal as a Steve McMahon shot cleared the cross bar with Martini impeded by the struggling figures beside him.
Extra-time looked a certainty despite Nick Tanner almost turning a Vashirua shot into his own goal before Walters provided the explosive finish.
Match-winner Walters paid tribute to the Kop after the historic win.
Walters insisted the volume of support from Liverpool's fans was crucial: "The fans were the vital factor. The noise they created put fear on the faces of the French players. You could see it. It was nice for us to give them something to shout about as we have had to take a lot of flak recently. We had a dream start with a goal after four minutes and didn't panic when it would have been easy to start pumping the ball upfield. We showed patience and got our reward."
Jubilant manager Graeme Souness also appreciated the value of the Mersey sound but also recognised the Herculean efforts of his players. He said: "Considering our injuries and the four foreigners regulation the performance was immense. In terms of the silky football this club is famous for, there wasn't much of that. But in terms of grit, determination and will to win I could not have asked for more. Everybody had written us off but we showed this club is made of sterner stuff than some people would have you believe. The crowd was superb, we have a young team and they need to know they have the backing of supporters. I feel more tired now than when I was playing on one of the old European night here."
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