You simply don’t come back from a 3-0 deficit against an Italian team. Not against the maestri of defensive soccer tactics. Impossibly, Liverpool did exactly that yesterday.

In a wonderfully dramatic final in Istanbul’s Ataturk Olympiat Stadium, Liverpool came back from the dead to outlast AC Milan and capture the 2005 Champions League title. It took overtime and a penalty-kick shootout to settle matters, but the huge trophy is now on its way to Merseyside, marking the fifth time that Liverpool has been crowned champion of Europe, and the first time since 1984.

Yet at halftime, with Milan playing fluently and confidently and deservedly leading 3-0 on goals by Paolo Maldini and a pair from Hernan Crespo, the game looked to be over. No team in tournament history had ever come back from 3-0 down to win. And we knew it wasn’t going to happen here, because Liverpool had shown nothing. Its attack was nonexistent, its defense full of holes, its goalkeeper Jerzy Dudek mishandling the ball. In the stands, the vacant, bewildered stares on the faces of the thousands of Liverpool supporters said it all.

The amazing revival began when coach Rafael Benitez made an obvious substitution, strengthening his midfield with Dietmar Hamann and taking off defender Steve Finnan. Rarely has a switch worked so perfectly and so immediately.

Eight minutes into the half, Liverpool got the simplest of goals – a left-wing cross into the Milan penalty area by John Arne Riise, and there was captain Steven Gerrard to arc a header over Milan goalkeeper Dida. Two minutes later, Vladimir Smicer scored to reignite the game.

Suddenly, the vaunted Milan defense, which had given up just six goals in its first 12 Champions League games, seemed a flimsy thing. Gerrard, so ineffective in the first half, sensed the moment. He went in for the kill, powering into the middle of the penalty area, the ball at his feet; only a clumsy tackle from Gennaro Gattuso stopped him, and Liverpool had a penalty kick. Spaniard Xavi Alonso took it, goalkeeper Dida parried it, but Alonso slammed the rebound into the roof of the net to make it 3-3.

That capped six incredible minutes for Liverpool, and those same fans were now chanting full blast, singing their unlikely anthem, a spot of American showbiz, “You’ll Never Walk Alone,” from “Carousel.”

Inevitably, the pace of the game slackened and caution began to take hold. There was to be no more scoring. The 30-minute overtime period arrived, and Milan substitute Serginho did his best to settle matters. In the first minute, his cross landed perfectly at the feet of Jon Dahl Tomasson, who made an awful mess of trying to get off a shot. Then, with only two minutes remaining, another perfect Serginho cross was headed powerfully down by Andriy Shevchenko – only for Dudek to make not one, but two remarkable saves as he somehow kept the header and the rebound out of the net.

After two hours of mostly exhilarating and remarkably clean soccer, it would have to be penalty kicks. On the stroke of midnight in Istanbul, the tiebreaker began, and was over almost as soon as it started.

Serginho blasted Milan’s first kick over the bar, while Dudek saved the second, from Andrea Pirlo. There will be controversy over that save, for Dudek had clearly, and illegally, moved forward about two yards before Pirlo struck the ball, but referee Manuel Enrique Mejuto Gonzalez saw nothing wrong. Hamann, Smicer, and Djibril Cisse scored for Liverpool, and it was up to Shevchenko to keep Milan’s hopes alive. He was kicking in the vital fifth slot because he’s Milan’s most reliable scorer – and no one was forgetting that he was the player who coolly shot home the winning goal when Milan beat Juventus on penalties for the 2003 title.

But this was not Shevchenko’s night. He had made little impact on the game itself, and now he blasted his kick right down the middle – and right into Dudek, who blocked it to give Liverpool a 3-2 penalty-kick victory.

An absurd, Hollywood-style victory if you like – for this was the same erratic Liverpool that could finish only in fifth place in the Premiership, meaning that, unless it gets a special dispensation from UEFA, it will not even qualify for next year’s tournament.

Sure enough, the English side got off to the worst possible start yesterday when Paolo Maldini put Milan ahead with only 50 seconds on the clock. Then in the 24th minute, Benitez’s gamble of starting the injury-prone Harry Kewell backfired when the Australian limped off, to be replaced by Smicer.

But Liverpool’s biggest headache was Milan’s Kaka. The Brazilian playmaker was running free in midfield, escaping his markers with consummate ease, and spraying seeing-eye passes in all directions. As the half neared its end, Kaka’s brilliance got its reward: From his perfect feed, Shevchenko swept the ball into the middle, where Crespo shot home. Six minutes later, Kaka hit a 35-yard ground ball that arrived, inch-perfect at the feet of the sprinting Crespo – his deft touch over Dudek made it 3-0.

A mere 75 minutes of soccer later, the stadium was a whirl of red-and-white confetti, and a vast, intimidating chorus of “You’ll Never Walk Alone” swept down from the stands as Gerrard first shyly kissed the trophy, and then let out a triumphant yell as he raised it into the night air.