Wolves climbed out of the relegation zone for the first time in three months and dumped West Ham in the bottom three to increase the pressure on manager David Moyes.
Daniel Podence scored the only goal when he drove home Matheus Nunes' cross three minutes after half-time.
Despite a summer outlay of £160m, West Ham have collected a single point from their past seven games before a meeting with Moyes' old club and fellow underachievers Everton at London Stadium next Saturday.
Moyes went to applaud the visiting supporters at the end but the reaction from many was negative.
He later said, "I think we could have taken more out of the game.
"We probably should have but ultimately we are not clinical enough in the final third. We did a decent job and we played much better in the second half than we had in the first half.
"But overall, I could not fault the players for their effort, we might fault them for the real quality we needed to get the goal.
"We should have done better on the counter-attack [for Wolves' goal] as we were the ones with the corner.
"And then they scored on the break, which is not good enough from our point of view.
"Even that took a deflection off Aaron Cresswell and goes into Podence's path to finish. Those small bits that you need to break for you, did not go for us today. And then, we had opportunities, we had chances with some headers, with crosses coming to the box but we never made them count.
"It's what we have been saying a lot this season, I don't think we have been playing terribly badly.
"But we have not been able to turn our good play [into goals]. We have not been able [to finish our chances].
"The players from our point of view have been great. But because of the standards we have set, the expectations we have set, it does not feel good."