David Moyes’ side need just a point from their last two matches against Backa Topola and Freiburg to finish at least second in Group A, and four to guarantee top spot, but they will be playing in Europe in some capacity in the new year.
West Ham struggled to break down Olympiakos until James Ward-Prowse chipped a precise pass over the opposition defence in the 73rd minute which was volleyed home by Pacqueta, who was adjudged to be offside until the VAR stepped in.
There was a tense atmosphere at the London Stadium with Group A hanging in the balance.
Said Benrahma tried to spark the sell-out crowd into life with a bending shot towards the top right corner that had to be pushed behind by Alexandros Paschalakis.
West Ham centre-back Nayef Aguerd caused problems at three corners, sending two headers wide and another straight at the goalkeeper.
Benrahma was again denied by Paschalakis while Lukasz Fabianski up the other end was untroubled, only seeing Daniel Podence’s volley drift off target.
The hosts were more patient on the ball in the second half yet created fewer chances. West Ham only saw Ward-Prowse scuff an effort at goal in the 63rd minute before Paqueta broke the deadlock.
Ward-Prowse’s perfect pass was met by a sweet, first-time volley from Paqueta, whose celebrations were cut short by the offside flag but then sparked again by the VAR.
West Ham, though, were let off by Olympiakos late in the game when Jackson Porozo flicked on a corner and the unmarked Camara stooped to head the ball against the left post.
I’m really pleased we got the result because that was most important. We didn’t play as well as we’d have liked but Olympiakos are a decent team, a well-seasoned European team that are used to coming away and being in these competitions – more so than we are.
“We made the best chances, they didn’t make too many opportunities to score. It was a little bit hairy a couple of times right at the end but apart from that we controlled most of it.
“It was a lovely ball from James (Ward-Prowse) and also the finish. We’d have two or three chances we didn’t take. We didn’t have many but in these games you don’t get too many.
“Thankfully, Lucas (Paqueta) came up with the goal.
I’m pleased with him as well because there are a lot of things he does that go unnoticed.
He did a lot of things tonight that weren’t as good as I’d have liked but the goal made up for it.”
It was a tough night for West Ham. Olympiakos executed their gameplan really well, made it tough for West Ham, there were no real chances for them. They couldn’t build up a head of steam.
“But around 70 minutes they carved out a fantastic goal.
It’s a great bit of play. How James Ward-Prowse executes the pass is fantastic.
A bit of backspin and then drops it over the defence in a line on the 18-yard box. He’s a really good technician.
“How Ward-Prowse doesn’t get recognised more by Gareth Southgate, it’s hard on him
Every set-play is always on the money. He goes about his job, so robust. Fantastic player.”