Lucas Paquetá's well-taken volley was the difference as West Ham United claimed a deserved 1-0 win over Olympiacos.
The Brazilian sweetly struck home from James Ward-Prowse's lofted pass on 73 minutes to net the only goal of the game in a closely-fought and gritty showing at London Stadium.
The Hammers had tested the Greek side prior to Paquetá's goal, with Nayef Aguerd going close from a corner while Ward-Prowse had also seen a first-time effort saved.
Olympiacos could have stolen a share of the points late on when Mady Camara's header hit the post, but the Irons held on for a hard-fought win.
Victory keeps David Moyes' side top of Group A on nine points from four games played.