Dominic Calvert-Lewin’s piece of brilliance ensured Everton secured a vital Premier League victory in their first game since the death of chairman Bill Kenwright.
On a poignant day for the Merseyside club, striker Calvert-Lewin turned his marker with a clever flick before firing low into the bottom corner.
It was a rare moment of quality in a scrappy encounter where both sides struggled to create chances.
Calvert-Lewin, who described Kenwright as a “great man” after the 78-year-old died on Monday, was the difference maker as Everton became only the fourth team to beat West Ham at home this year.
However, the Toffees needed keeper Jordan Pickford to be alert in stoppage time in order to clinch victory.
The England international barely had a save to make before beating away a fierce volley from Hammers substitute Said Benrahma.
Everton move five points clear of the relegation zone, climbing above Nottingham Forest – who lost 3-0 at Liverpool – on goal difference to sixth from bottom in the table.
West Ham, who stay ninth, have won just one of their past six Premier League games as their strong start to the season continues to fade.