He picked up possession 25 metres out, jinked past midfielder Michael Carrick and sent a curling left foot shot round defender Rio Ferdinand and into the bottom corner of the net.
"To beat a great side like United, the way we did, is something very special and I can't hide the joy and pride I feel for my players," said Olympiakos coach Michel.
"We picked the best moment to show Greek football is alive and kicking," added the former Spain and Real Madrid striker.
"I'm surprised, I didn't see that level of performance coming.
Strike pair Wayne Rooney and Robin van Persie were peripheral figures for the visitors as pot shots on goal from Giannis Maniatis and Hernan Perez lifted the home supporters.
United, the European champions in 1968, 1999 and 2008, were punished again for poor defending 10 minutes into the second half.
Defeat at the Georgios Karaiskakis Stadium represented yet another body blow in an inauspicious campaign Puma High Tops Mens
Alejandro Dominguez opened the scoring with a clever first half flick and Arsenal loanee Joel Campbell added a sublime second goal to leave United facing a huge task to overturn the deficit in the return match at Old Trafford on March 19.
Moyes sent on Danny Welbeck and Shinji Kagawa for Valencia and Cleverley but it was more a change in attitude than personnel that was required from United.
Moyes's men looked sluggish and disjointed against an inexperienced Olympiakos side who are bidding to reach the quarter finals for only the second time in their history.
Midfielder Tom Cleverley registered United's only effort of note in the first half with a 17th minute half volley that sailed high over the bar.
Moyes sees red after United loss
Olympiakos, wearing bright red and white jerseys, red shorts and socks, broke the deadlock seven minutes before halftime with a smart piece of improvisation from Argentine forward Dominguez.
Moyes opted to start with two wingers, Antonio Valencia and Ashley Young, but neither made an impact in a first half in which runaway the Greek league leaders displayed real energy and hunger.
for last season's English Premier League title winners.
"That's the worst we've played in Europe. We didn't deserve to get anything," manager David Moyes told reporters. Puma Pink
Patrice Evra's half hearted clearance from a corner landed at the feet of Maniatis 25 metres out and his tame, low shot was expertly diverted past keeper David De Gea by Dominguez's flick.
Campbell, who is likely to feature for Costa Rica against Group D rivals England at the World Cup in Brazil in June, did the damage.
"It is a great moment for us and we will enjoy it but we must look ahead to the second leg. Whoever thinks 2 0 is enough to qualify is mistaken," said Michel.
"I take responsibility, we have to play better. The players are hurting."
a thread after they produced an abject display to lose 2 0 at Olympiakos Piraeus in a Champions League last 16 first leg on Tuesday.
Manchester United's dwindling hopes of lifting a trophy this season are dangling by Puma Shoes Blue And White
After a cautious opening from both sides amid ear splitting noise from an Puma Shoes Womens 2017 enthusiastic home crowd, the first chance fell to Olympiakos as Dominguez burst through the middle on a solo run only to be denied by a last ditch tackle from Nemanja Vidic.
It was the first time the Greeks had beaten United in five attempts.
Dutch striker Van Persie summed up his team's night with five minutes to go. He received the ball 12 metres out and turned inside a defender before blazing a right foot shot way over the bar.
United are out of the FA Cup and the League Cup and trail Premier League leaders Chelsea by 15 points with 11 games left to play.
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