Substitute Andy Cole ensured the win with a second goal on 82 minutes.

Inside the opening seconds, Paul Scholes suffered a rush of blood when he aimed a kick at Stylianos Venetidis.

Fortunately he missed the defender and his act of petulance was unnoticed by Italian referee Graziano Cesari.

Scholes’ team-mates demonstrated much more composure and they quickly settled into their passing game.

Denis Irwin briefly left the pitch for some treatment after he collided with the Brazilian Giovanni.

Both sides had a couple of pot shots and Roy Keane fired over for United while Olympiakos skipper Stylianos Giannakopoulos saw a drive from the edge of the D deflected for a corner.

Predrag Djordjevic swung the corner into the near post where ex-Middlesbrough midfielder Christian Karembeu met the ball with a glancing header over the bar.

After these few jabs, Olympiakos should have landed the first telling blow of the contest in the 15th minute.

Djordjevic curled a free-kick into the United box and the unmarked Giannakopoulos headed wide from no more than seven yards out.

With both teams packing the midfield, the middle of the park was as congested as Athens’ gridlocked streets.

Olympiakos knew they could not risk conceding free-kicks anywhere near the box after Beckham’s great strike on Saturday.

However Djordjevic demonstrated that he, too, can be dangerous from free-kicks and he drilled one from the right-hand side of United’s box just over Fabien Barthez’s bar.

Giannakopoulos was not having a good night in front of goal and on 28 minutes he missed another gilt-edged chance.

Djordjevic whipped in a deep free-kick and caught United’s defence doing impersonations of the statues that grace the ruined Parthenon only for Giannakopoulos to direct his volley straight at Barthez, who made a reflex save.

The game was opening up and two minutes later Ryan Giggs teed up Juan Veron, who had flown in from Paraguay to play, to shoot just wide.

Giggs then unlocked the home side’s defence with a sliderule pass to Paul Scholes only for Olympiakos goalkeeper Dimitrios Eleftheropoulos to save at the England midfielder’s feet.

Giggs turned creator again just before half-time when he released Veron on the right and the Argentine’s shot was blocked by Eleftheropoulos.

Beckham lined up a free-kick from around 30 yards out only for him to curl it into the arms of Eleftheropoulos.

United sensed they were close to a breakthrough after the interval and Karembeu nodded away Laurent Blanc’s goalbound header to the dismay of the veteran Frenchman.

Giovanni had had a quiet game and the Brazilian briefly raised the hopes of the Olympiakos fans when he stood over a free-kick - only for him to bend it over Barthez’s goal.

That just about summed up Olympiakos’ attacking threat and United were dealing comfortably with what little danger they posed.

United were in control and it came as little surprise when they took the lead on 65 minutes through man of the moment Beckham.

Giggs swivelled and sent over a delightful cross to the back post where Beckham came running in to direct home his sixth goal of the season.

Two minutes later United could have had a second when Giggs’ header from Beckham’s cross was brilliantly saved by Eleftheropoulos with his outstretched right hand.

Alex Ferguson then decided to substitute jetlagged Juan Sebastian Veron and bring on Andy Cole - the switch proved inspirational.

The substitute combined with van Nistelrooy and after exchanging passes Cole had the easy task of rolling the ball into the net.

United's night got better as Lille equalised with Deportivo La Coruna in the final minutes of their game in France to leave United on top of their group.