While the hapless Hammers failed to take any of the handful of decent chances that came their way, it was left to Jørgen Strand Larsen to show them the way to goal with his first-half winner.
The Norwegian striker netted for the 10th time this season to give 17th-placed Wolves a victory that sent them a dozen points clear of the dreaded drop zone and just five adrift of West Ham, who sit just one rung above Vitor Pereira’s side in the Premier League table.
“It was a game of a few big chances and, unfortunately, we didn’t take any of the ones that came our way,” grimaced Graham Potter, who had handed full debuts to Luis Guilherme and Evan Ferguson.
“It’s about the team playing well and getting as many points on the board as we can and we just haven’t done that tonight.”
Certainly, it might have been a different story had Ferguson converted on the quarter-hour mark but the on-loan Brighton & Hove Albion forward – just eight yards out – miscued Jarrod Bowen’s inviting low cross and Matt Doherty cleared off the line.
That proved costly as, after Toti’s stooping header was brilliantly tipped aside by an athletic Alphonse Areola, Larsen beat the French keeper on 21 minutes with a powerful 20-yarder that deflected off former Wolves’ skipper Maximilian Kilman after Konstantinos Mavropanos had failed to clear the danger.
With the visitors now on the back foot, Marshall Munetsi also rocked the crossbar leaving Potter to make a triple switch at the break, introducing Niclas Füllkrug, Edson Álvarez and Carlos Soler in place of the crestfallen Ferguson, anonymous Guilherme and third central defender, Aaron Cresswell.
“I wasn’t happy with our general play in the first-half,” added Potter having changed formation.
“We had that very good chance but then got pushed back too much. Evan is learning that he needs to take the not-so-good times as well as the better ones but he’s got good team-mates around to help him through these moments.”
Replacement Füllkrug, returning from a hamstring injury that had kept him out of action since early January, had certainly looked rusty when he did all the hard work in front of goal before somehow slicing his final shot towards the touchline.
But the 22-cap German striker almost redeemed himself with a header that looped onto the crossbar before fellow second-half substitute Emerson bundled the rebound wide.
“The more Niclas plays, the better he’ll get,” insisted Potter.
“We’ve been trying to build him up behind closed doors but that’s obviously a lot different to coming straight back into the Premier League after a bad injury.
"I’ve been very impressed with him - he gives us different options because he plays more vertically and has strength, touch and intelligence, too. Niclas is a big personality and once he’s fully-fit, he’ll certainly help us.’’
Another recently-arrived substitute - Tomáš Souček – also went close to salvaging a late point in a feisty finale but the Czech Republic midfielder skewed his angled shot wide of the near post on a miserable Molineux night, when the Hammers were simply destined not to score.
“We were a lot better in the second half and we managed to push Wolves back but overall we’ve got to perform better as a team,” concluded Potter, whose side now face Bournemouth at London Stadium on Saturday (3pm).