Saturday’s 1-0 win at Chelsea bought Pellegrini some time but the Hammers reverted to type at Molineux on Wednesday.
While they remain 13th West Ham sit just two points above the relegation zone ahead of Monday’s London derby with Arsenal.
Victory, though, sent Wolves back to fifth in the Premier League and Nuno Espirito Santo’s side are unbeaten in 10 top-flight matches for the first time since January 1972.
Saturday’s shock win at Stamford Bridge had breathed new life into the Hammers but after their recent run they found themselves in a more familiar position just 23 minutes in.
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Leander Dendoncker scores the opener (David Davies/PA)
It had been a quiet opening, with Molineux flat, but Wolves took advantage of some sloppy West Ham defending to open the scoring.
Joao Moutinho swung in a corner and Dendoncker beat Ryan Fredericks to the ball to stab in from six yards.
David Martin’s only other job, other than picking the ball out of his net, had been to tip over Raul Jimenez’s looping effort a few minutes earlier.
Declan Rice’s header was gathered by Rui Patricio as the visitors mounted a response before Pablo Fornals forced the goalkeeper into a fine save.
Manuel Pellegrini’s side were well beaten (David Davies/PA)
The midfielder cut inside after collecting the ball on the left but his curling effort from 16 yards was palmed out.
Wolves continued to look the more dangerous though and Martin beat away Diogo Jota’s drive 10 minutes before the break.
The hosts remained on top after the restart and Dendoncker headed over and Martin saved Jonny’s close-range effort.
But Robert Snodgrass wasted a fine chance to level on the hour when he failed to control Fornals’ deep pass with just Patricio to beat.
To make matters worse the winger was forced off after colliding with the goalkeeper and was replaced by Andriy Yarmolenko.
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