Taty Castellanos struck twice inside two minutes midway through the second half to add to Konstantinos Mavropanos's first-half header before the defender volleyed in again late on.
Nuno Espirito Santo's team shrugged off early nerves to blow away the league's bottom side and push their rivals from north London closer towards the unthinkable.
The Hammers had looked buried after losing at home to Nottingham Forest in January with defeat to their relegation rivals leaving them then winless in 10 and seven points adrift of safety.
But five victories in the 11 games since, together with Spurs' apparent free fall, have put a radically different complexion on the picture at the bottom.
Against Wolves, they were wasteful in the first half. Mavropanos's opener, headed in from Jarrod Bowen's cross three minutes before the break, lifted the atmosphere at a crucial moment and set the second-half stage for Castellanos to double his tally for the club and inch West Ham towards survival.Â
"We are extremely happy," Hammers coach Santo said. "All of us deserve an evening like this, especially our fans.
"London Stadium was amazing; it was bouncing with energy even in the hard parts when the game was tough.
"I realise there is still a lot of work to be done yet. We made a big step today, which was important for us, but nothing has changed."
The result ended Wolves' brief revival after three games unbeaten. Relegation for them could now be confirmed as early as next week away to Leeds.
