Nuno Espirito Santo’s side took the lead through Konstantinos Mavropanos’ first-half header at the London Stadium.
Valentin Castellanos netted twice in the second-half to ensure fourth-bottom West Ham, who started the evening in the relegation zone, moved two points above third-bottom Tottenham.
Mavropanos completed the rout with his second goal in the closing stages in an ironic twist as the former Arsenal defender helped to push his old club’s bitter rivals closer to the drop.
It is the first time Tottenham have been in the bottom three at the end of a Premier League match-day since August 2015, when they lost 1-0 to Manchester United.
Tottenham can climb back out of the relegation zone if they win at Sunderland in Roberto De Zerbi’s first game in charge on Sunday.
The north Londoners have seven games to save themselves from playing in the second tier for the first time since 1977-78.
Beaten on penalties by Leeds in the FA Cup quarter-finals last weekend, West Ham bounced back with a vital victory in their own fight for survival.
“All of us deserve this kind of evening, especially our fans. London Stadium today was amazing, bouncing with energy,” Nuno said.
“The first half was tough. We didn’t find spaces, the game didn’t flow. Then after the break we really improved.
“The way we did it proved to ourselves that we cannot give up. That was the team spirit from the beginning.
“We are in the fight. I realise we have a lot of work to do yet. We made a big step today, important for us, but nothing has changed.”
Bottom of the table Wolves are 15 points from safety and, with only six matches left, they are destined for relegation to the Championship.
Wolves looked rusty in their first game for 25 days due to the international break and their exit from the FA Cup.
El Hadji Malick Diouf’s poor pass gave Adam Armstrong a sight of goal, but the Wolves striker couldn’t keep his effort on target.
Armstrong wasted a better chance moments later when his close-range header was saved by Mads Hermansen.
West Ham took advantage of those escapes to steal the lead in the 42nd minute.
Replays showed West Ham were lucky to be awarded a corner when the final touch came off Jarrod Bowen and the England forward quickly rubbed salt into Wolves’ wound.
When Bowen’s corner was headed back to the forward, he produced a far better cross with his second attempt and Mavropanos rose to thump his header past Wolves keeper Jose Sa.
Bowen hit the post with a dipping curler early in the second half and Castellanos delivered the knockout blow in the 66th minute.
Playing a one-two with Pablo, the Argentine striker surged through the Wolves defence but his tame shot should have been saved by Sa before it trickled over the line.
Castellanos struck again two minutes later with a deflected shot that squirmed past the hapless Sa.
Mavropanos volleyed home at the far post from an 83rd minute corner to compound Wolves’ misery. (AFP)
