West Ham lost 2-1 away to the Greek side a fortnight ago but their win at the London Stadium put them level on nine points with second-placed Freiburg, who crushed bottom side Backa Topola 5-0.
"If I was being honest, I don’t think we made enough chances or opportunities and I need to look to see why that was the case," West Ham manager David Moyes said.
The West Ham fans then held their breath late on as the visitors nearly equalised when Mady Camara's close-range header struck the post when he should have scored.
Marseille secured a second victory with their win in Athens thanks to goals from Chancel Mbemba and Ismaila Sarr.
The Italians are unbeaten in Group D on 10 points, three ahead of Sporting who beat 10-man Rakow Czestochowa 2-1.
Persons:
Ham United's Lucas Paqueta, Said Benrahma, Emerson Palmieri, Vladimir Coufal, Isabel Infantes, David Moyes, Paqueta, James Ward, Prowse, Mady Camara's, Mbemba, Sarr, Jarell Quansah, Alexis Mac Allister, Klopp, Atalanta, Berat Djimsiti, Pedro Goncalves, Bogdan Racovitan, Danilo Pereira, Todd Cantwell, Janina Nuno Rios, Tommy Lund, Ed Osmond, Ken Ferris
Organizations:
Soccer, Europa League, Ham United, Olympiacos, London, REUTERS, Olympiakos Piraeus, Olympique de Marseille, AEK Athens, West Ham, Backa, Olympiakos, Marseille, Ligue, Brighton & Hove Albion, Ajax Amsterdam, LIVERPOOL, Liverpool, French, Toulouse, Sturm Graz, Berat, Sporting, Rangers, Sparta Prague, Real Betis, Aris Limassol, Betis, Thomson
Locations:
London, Britain, Freiburg, Ham, Athens, European, Czestochowa