Richarlison was Everton’s hero as Sheffield United’s Europa League dream was in tatters on Monday night, while Brighton guaranteed their Premier League survival with a goalless draw against Newcastle.
The Blades were handed a second successive defeat as Brazil forward Richarlison struck the only goal early in the second half at Bramall Lane.
Chris Wilder’s side remain in eighth place, two points behind seventh-placed Wolves who hosted Crystal Palace later on Monday.
United’s hopes of capping a memorable first season back in the Premier League with a Europa League berth will be over if Wolves beat the Eagles.
The teams who finish fifth and sixth are certain to reach next season’s Europa League.
If the FA Cup winners finish in the top six, then seventh place would also qualify for the Europa League.
Arsenal, who face third-placed Chelsea in the FA Cup final, are currently 10th.
Everton striker Dominic Calvert-Lewin went closest to breaking the deadlock in the first half as his header struck a post.
Carlo Ancelotti’s team won it in the 46th minute when Richarlison met Gylfi Sigurdsson’s free-kick with a glancing header for his 15th goal of the season.
At the Amex Stadium, Brighton got the point they needed to be mathematically certain of avoiding relegation.
Graham Potter’s side were already virtually certain to stay up because their goal difference is far superior to third-from-bottom Aston Villa — the only team in the relegation zone who could catch them.
Brighton have won just two of their last 17 league games, but ending a run of three successive home defeats moves them seven points clear of the bottom three, with Villa having just two games left.