The glory of Liverpool is reborn. They are champions of Europe after winning a shoot-out 3-2, with the decider struck by Vladimir Smicer and confirmed by Jerzy Dudek's save from Andriy Shevchenko. But it had taken a near miracle from them to send this match into extra-time. Even there, Dudek, with three minutes left, made a double save from Shevchenko that was all but inconceivable. Liverpool's exhilarating powers of recovery, after being 3-0 behind at the interval, inspired the greatest European Cup final of modern times.

Against all sense, their goals all came in a six-minute spell as they mangled a defence billed as the world's best. That had been beyond conception after Paolo Maldini's opener in the opening seconds and two more goals by Hernán Crespo.

The Argentinian, on loan from Chelsea, could never have guessed that he would be substituted not to enjoy a personal ovation, but because Steven Gerrard, Smicer and Xabi Alonso had put Liverpool on level terms. No one could have conceived of it, except for the Anfield players.

Liverpool were in a final they had scarcely expected to reach and felt for much of the evening that they did not belong there. The encouragement then lay not on the field but in the stands, where the great, undiscouraged believers in this club rallied in remarkable numbers. They had come so far to will their side to triumph but at first were forced to admire the technique and style of Carlo Ancelotti's side.

Milan's immediate breakthrough disrupted an acclimatisation process that had scarcely begun. The goal had something to do, as well, with stagefright in the English side that let their opponents strut the boards. The extraordinary comeback was beyond imagination then.

Djimi Traoré fouled Kaka in the first minute, but the position of the free-kick was not one that would normally make Liverpool quake. Rafael Benítez's men had been well marshalled to stifle Chelsea in the last four, but on this Istanbul evening there was a distracted quality to the marking.

Andrea Pirlo pulled his free-kick slightly behind the main group of attackers and the 36-year-old Maldini hit it hard enough with his right foot from 12 yards to ensure that it flew past Jerzy Dudek on the bounce.

The goalkeeper was beaten twice more before the interval but actually showed a level of aplomb that looked beyond conception for Liverpool. Xabi Alono and Steven Gerrard were left on the sidelines of a midfield full of marvellously articulated moves.

Liverpool were earnest and dogged but there was scant sophistication or cohesion. Minds left in a spin by Maldini's goal took time to steady.

Crespo met a corner in the 14th minute with a header that was blocked on the line by Luis García, well before he got on with scoring.

The first of his goals was traumatic for a Liverpool side already feeling victimised. García had shot wide and then, speculatively, claimed a penalty when he forced the ball against Alessandro Nesta, who had gone to ground, but Milan counter-attacked ruthlessly.

Clarence Seedorf found Kaka and his beautiful pass inside Traoré let Andriy Shevchenko set up Crespo to score at the far post. A minute before half-time, Kaka again split the Liverpool defence with a raking ball and Crespo was on the loose to dink it stylishly over Dudek.

Fans will normally warm to any hint of flamboyance, but there was, as it turned out, a justified ambivalence here about the selection of Harry Kewell. The Australian is at risk of being classified as one of those footballers who is too expensive to be off-loaded.

Naming an attacker whose form is so unpredictable was a cavalier gesture from the roundhead Benítez. Kewell lasted only 23 minutes before going off with a groin strain but his inclusion had its effect, too, on the rest of the team. In particular, it cost Dietmar Hamann his place in the starting line-up, even though it had taken Jamie Carragher to deny him the man-of-the-match award in the semi-final win over Chelsea at Anfield.

Maybe Milan became complacent or, more likely, Liverpool found an urgency inspired by desperation. Facing humiliation, they reacted with so much pride that they created one of the greatest periods in the extraordinarily rich history of this club.

It all started nine minutes after the interval when John Arne Riise crossed from the left and Gerrard climbed to head home. Milan's marking was as lax then as Liverpool's had been at the outset and the consequences were just as extreme. This time it was Ancelotti's turn to gaze in disbelief.

Milan had no chance to regain their poise. All the confidence was Liverpool's as they passed the ball along the edge of the penalty area four minutes later until Hamann put it into the path of his fellow substitute Vladimir Smicer. From 20 yards he drilled a low finish across and beyond Dida.

This was almost certainly the last match for Liverpool of a Czech international who has come to the end of his contract, but this game obliterated the past and the future. A rout had turned into a contest full of compulsive action.

The play roared towards a Liverpool equaliser. All the gaps were in the Milan side as Gerrard drove straight through the middle until Gennaro Gattuso brought him down for a penalty. Dida leapt to his right to save Alonso's kick but the Spaniard smashed in the rebound with his left foot.

The ball had run kindly to him, but all credit was due to Liverpool for making this game alter course and turn back in their favour.

· Fears that the Ataturk Olympic Stadium would prove unfit to stage the final appeared justified last night. The lack of public transport, adequate infrastructure and basic preparations left Uefa officials privately embarrassed at the choice of stadium. Chaotic traffic policing saw one access road closed, stretching journey times to three hours and technicians battled power cuts while struggling to connect telephone lines for reporters and broadcasters in time for kick-off.

Milan (4-3-1-2): Dida; Cafu, Nesta, Stam, Maldini; Gattuso (Rui Costa, 112), Pirlo, Seedorf (Serginho, 86); Kaka; Shevchenko, Crespo (Tomasson, 86). Subs not used: Abbiati, Kaladze, Costacurta, Dhorasoo.

Liverpool (4-4-1-1): Dudek; Finnan (Hamann, h-t), Carragher, Hyypia, Traoré; García, Alonso, Gerrard, Riise; Kewell (Smicer, 23); Baros (Cissé, 85). Subs not used: Carson, Josemi, Núñez, Biscan.

Booked: Carragher, Baros.

Referee: M E Mejuto González (Spain).