Substitute Gianluca Scamacca scored the winner against Anderlecht as West Ham recorded a third straight victory in the Europa Conference League.
Scamacca guided it into the bottom corner with a first-time strike on the turn, late in the second half.
West Ham goalkeeper Alphonse Areola was forced to make an excellent save to block Anderlecht striker Fabio Silva's header shortly afterwards.
The Hammers sit top of Group B with Anderlecht five points behind.
Hammers boss David Moyes later said: "I'm very pleased with a win and clean sheet away from home.
"Anderlecht hadn't conceded any goals in the group stage previously, so it was always going to be tight. We missed a hatful of opportunities to score and made it a bit scary for ourselves, but overall I thought we deserved the victory.
"I don't think you're seeing anybody win by big margins in this competition, football throughout Europe is really competitive and it was another tough game tonight.
"Alphonse's save near the end was incredibly crucial.
"But let's be fair, if they had scored then I don't think [the result] would have been correct. I thought we had done enough to score more on the night.
"I have to say, though, he's playing really well for us and he's done a great job tonight."