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.