Deep in the thick of a relegation battle, three points felt like a necessity for West Ham given that Spurs were facing already-relegated Wolves.
They certainly started like a side who knew there was plenty riding on this clash too, flying out of the traps and coming close inside the opening 10 minutes when Crysencio Summerville planted a perfect cross onto the head of Tomas Soucek, but the Czech could only head narrowly over the bar.
The Hammers controlled most of the first half, but did so largely without threatening the Everton goal too much, which would have been of concern to boss Nuno Espirito Santo.
A tame first half ended with Jarrod Bowen dragging an effort across the face of goal for the hosts, and his uncharacteristically poor effort was symptomatic of the struggles both sides faced in the first half, particularly West Ham, who failed to muster a single shot on target.
That all changed within minutes of the restart though, as Taty Castellanos tested Jordan Pickford, with West Ham believing they should’ve had a penalty for a foul in the aftermath.
Disappointment soon turned to ecstasy as from the resulting corner, Soucek climbed highest inside the area to head home Bowen’s corner and fire the Hammers ahead.
The goal didn’t exactly spark Everton into life, as they looked very much like a side with precious little to play for for most of this game despite their proximity to the European places.
They eventually picked up, and a penalty box scramble which saw a big block from Soucek was followed up by a huge clearance from Axel Disasi as West Ham clung to their slender one-goal lead.
Thierno Barry came close to finding a leveller for the visitors when his header was heroically cleared off the line by man of the moment Soucek, whose goal looked to be enough to secure all three points.
That was at least until Kiernan Dewsbury-Hall was in the right place at the right time to volley home James Tarkowski’s knockdown in the 88th minute to seemingly send West Ham into the drop zone.
An otherwise drab affair had yet one more crazy twist though, as in eight minutes of stoppage time, Wilson popped up to send the London Stadium wild with a late winner which ensured West Ham maintained their two-point lead over Tottenham in the race to avoid relegation.