Billed as Manchester United's greatest European challenge, that is exactly what it proved to be as they were taught a Champions League lesson by Real Madrid and the irrepressible Ronaldo.

The Brazilian striker, who lit up the World Cup final with his finishing prowess, may have lived in the shadow of team-mate Raul for much of this season since his arrival from Inter Milan.

But with his fellow striker injured, Ronaldo rose to the occasion in the manner of a true champion as he struck a hat-trick of the highest quality to earn a rousing ovation from the Old Trafford crowd.

To their credit, United never once gave up and emerged with their pride intact as they actually won on the night, even if they fell two goals short of actually going through to the semi-finals.

David Beckham even emerged from the bench - clearly with a point to prove - to strike twice amid a spirited attacking display by his side in a mesmerising game of seven goals and countless chances.

However, Champions League glory is achieved as much by defensive resilience and European nous as sustained attacking pressure.

Real may have their weaknesses but United, trailing 3-1 from the first leg, were made to pay for their deficiencies at the back as this proved a revival beyond even the supposed comeback kings.

Ruud van Nistelrooy pulled United back into the tie in Madrid and struck again at Old Trafford to equalise Ronaldo's first strike after just 12 minutes.

However, that opening goal by the Brazilian always left United with a mountain to climb and when Ronaldo struck again shortly after the break, there was no way back.

Just as in Madrid a fortnight ago and just as against Real at Old Trafford in 2000, they had been made to pay for naively piling forward and leaving themselves exposed at the back.

Ivan Helguera's own goal revived faint hopes but Ronaldo completed his hat-trick before Beckham came off the bench to convert a free-kick and then force his side's fourth goal over the line.

Real were nevertheless home and dry, with the team taunted by United as "performing seals" having proved they have the steel and class to match their tricks.

United's task had been to prove they had learned to modify the gung-ho mentality which cost them dearly three years ago in going out to Real on an eerily similar occasion.

It was not to be. Van Nistelrooy forced Madrid goalkeeper Iker Casillas into an early reaction save but, predictably enough, it was just when United were threatening that Real hit them on the break.

With Wes Brown lured upfield, Steve McManaman - preferred to Flavio Conceicao in midfield - started the move that led to Guti setting Ronaldo through the centre.

Ronaldo looked to be closely watched by Rio Ferdinand but appearances were deceptive as the striker brushed past his marker with embarrassing ease before burying his shot.

United were badly ruffled but, with Real continuing to threaten through Luis Figo, Ivan Helguera and Roberto Carlos, they at least bided their time.

Such patience finally paid off as the Spanish side were lulled into a false sense of security and allowed their tempo to drop 10 minutes before the break.

That was the cue for United to come alive as Ryan Giggs shaved the post and Ole Gunnar Solskjaer had a smart shot blocked by Casillas before the two players combined to set up van Nistelrooy from close range.

Finally there was renewed hope. With Helguera limping badly, Real looked distinctly vulnerable and van Nistelrooy almost pounced again.

The Spanish side nevertheless held out until half-time and, rather than remaining patient after the restart, United were naive enough to pile into attack and were duly punished.

After one warning had been ignored, with Figo curling a shot against the post, Real pounced as Roberto Carlos set up Ronaldo - in acres of space - to beat the exposed figure of Fabien Barthez.

That was the killer blow, but a mis-hit shot by Juan Sebastian Veron still somehow forced Helguera into striking his clearance into his own net.

To their credit, United refused to give up, with Solskjaer and Veron both being denied by Casillas' reactions.

However, their finishing was simply not in the same league as that of Ronaldo, who responded by giving Barthez no chance at all as he picked his spot from 20 yards out.

The result may have been beyond doubt but Beckham clearly had a point to prove and took delight in converting a curling free-kick with customary aplomb.

The final stages represented something of an exhibition game, with substitute Javier Portillo striking the side-netting from point-blank range and Beckham then forcing the ball home.

For all of the glorious excitement, United eventually ended the night as they began it, within two goals of victory.

The simple truth remains that they were beaten by a better side - and one surely destined to return to Old Trafford in the Champions League final in just over a month's time.

Teams:

Man Utd Barthez, O'Shea, Ferdinand, Brown, Silvestre (Phil Neville 79), Veron (Beckham 63), Butt, Keane (Fortune 82), van Nistelrooy, Giggs, Solskjaer.

Subs Not Used: Ricardo, Blanc, Forlan, Fletcher.

Booked: Veron, Fortune.

Goals: van Nistelrooy 43, Helguera 52 og, Beckham 71, 84.

Real Madrid Casillas, Salgado, Hierro, Helguera, Carlos, Zidane, McManaman (Portillo 69), Figo (Pavon 88), Makelele, Ronaldo (Solari 67), Guti.

Subs Not Used: Cesar, Morientes, Flavio, Cambiasso.

Booked: Figo.

Goals: Ronaldo 12, 50, 59. Agg (5-6)

Att: 66,708

Ref: Pierluigi Collina (Italy).