Sheffield United's hopes of playing European football next term were dealt a blow as they lost at home to Everton in their penultimate game of the Premier League season.
Richarlison scored the game's only goal early in the second half when he glanced home a header from Gylfi Sigurdsson's free-kick.
That strike brought the game to life after a dire first half in which Dominic Calvert-Lewin had the only real chance, but his header hit the post.
David McGoldrick was denied a immediate response for Sheffield United when his low drive inside the box was blocked, but the Blades looked distinctly off key throughout.
Instead it was Everton who looked the most likely to add to their lead as Calvert-Lewin brought a save out of Dean Henderson before Andre Gomes drove just wide of the post in the closing stages.
The defeat for Sheffield United ended their slim hopes of finishing in the top six as they sit four points behind sixth-placed Tottenham with one game remaining.
They will now have to win their final game of the season at Southampton and hope Wolves lose both their remaining games - and Chelsea win the FA Cup - to secure a place in next season's Europa League.
The win for Everton moved them above Southampton and into 11th.
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Sheffield United boss Chris Wilder was hugely critical of his players after the 2-0 defeat by Leicester last time out, calling them League One and Championship players playing in the Premier League.
The 52-year-old is known for his tough love approach to management - an attitude that has helped his squad play beyond their perceived individual ability this season.
Wilder clearly expected a positive reaction as he named the same side that started in that Foxes defeat. There was plenty of huff and puff from his players against the Toffees but they lacked quality in the final third.
There was also a distinct lack of urgency, with the toils of a long but hugely impressive first season back in the Premier League looking like it is starting to take its toll.
They pressed in the final few minutes as Everton sat back but finished the game without mustering a shot on target.
Regardless, Sheffield United have one game remaining of a superb season and they can be proud of their efforts, whether they secure European football next season or not.
Richarlison underlines importance to Toffees
This was a much needed win for Everton with their season having looked in danger of fizzling out in disappointing fashion.
A run of two wins and a draw after the restart was followed by a four-game winless run that ended their hopes of a top-10 finish.
Carlo Ancelotti approached this game with one eye on next season, assessing his options from the club's youth team by handing promising 18-year-old defender Jarrad Branthwaite his first Premier League start while 19-year-old forward Ellis Simms was included on the bench.
But whatever changes Ancelotti decides to make to his squad over the summer, this game underlined the importance of Richarlison to the Toffees' aspirations next season.
He was one of the few players for either side looking to make something happen in a dull first half with some determined runs, while it was his goal - a superbly guided header after a clever run - that finally provided the spark the game needed.
Richarlison has scored 15 goals so far this season - 14 of those coming in the Premier League - an impressive return in a difficult campaign for Everton in which they had looked in danger of being involved in a relegation battle before Ancelotti's arrival in December.
A full pre-season working with the Italian and the Brazilian has a real chance of developing into a 20-goals-a-season striker next term.
Man of the match - Richarlison (Everton)
What next?
Sheffield United complete their Premier League campaign with an away trip to Southampton on Sunday, 26 July (16:00 BST), while Everton host Bournemouth at the same time.