Daniel Jebbison became the youngest player to score on his first Premier League start with a winning goal that dealt a blow to Everton's European ambitions.
Jebbison, aged 17 years and 309 days, fired Sheff Utd ahead on seven minutes when he steered home Jack Robinson's inviting cross.
He could have added a second on 34 minutes but his initial chip was saved by Jordan Pickford and when Ben Osborn returned the ball, Jebbison's second shot was blocked by Ben Godfrey.
At the other end Aaron Ramsdale, who had already denied Allan, produced a superb double stop just before half-time, firstly from Richarlison's diving header before clawing away Dominic Calvert-Lewin's follow-up from two yards.
Ramsdale made another important save on 71 minutes, tipping Richarlison's shot around the post.
David McGoldrick and John Egan went close to doubling Sheff Utd's lead as they held on for their sixth win of the season.
Defeat leaves Everton eighth, seven points off fifth-placed Liverpool. Sheff Utd remain bottom on 20 points.
See: Everton report | Sheff Utd report
Next fixtures
Everton: 19 May v Wolves (H)
Sheff Utd: 19 May v Newcastle (A)
Match officials
Referee: Jonathan Moss. Assistants: Marc Perry, Timothy Wood. Fourth official: Lee Mason. VAR: Simon Hooper. Assistant VAR: Peter Kirkup.
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