Jean-Philippe Mateta salvaged a point for Crystal Palace and put a dent in Everton’s European hopes with a late strike against the Toffees.
The French forward came off the bench to pull Oliver Glasner’s side level with a 77th-minute strike after Beto had restored Everton’s lead early in the second half.
Ismaila Sarr earlier cancelled out Everton defender James Tarkowski’s sixth-minute opener as Everton missed a chance to nudge up to ninth in the table.
There is a scenario where eighth could be enough to qualify for Europe depending on the outcomes of this season’s continental competitions and the FA Cup final between Manchester City and Chelsea.
So this was a big opportunity for Everton to move level on points with eighth-placed Brentford before their final two games, but the draw means they sit 10th for now.
Everton went ahead when Tarkowski shot home from close range after Kiernan Dewsbury-Hall’s corner from the right was flicked on to the back post.
After booking their place in the Conference League final with victory over Shakhtar Donetsk on Thursday night, Palace’s focus is clearly on European matters rather than their remaining Premier League games.
However, manager Glasner made just two changes from the win over Shakhtar, signalling intent to get a result here with their first European final not until three days after the domestic season ends.
Sarr got the hosts level at Selhurst Park in the 34th minute when his deflected effort on the rebound found its way past Jordan Pickford.
But two minutes into the second half, Everton were back in front.
A long pass from Tarkowski put Beto on the ball and running towards goal. The striker managed to hold off Maxence Lacroix before turning the Palace defender and sliding the ball through the legs of Eagles goalkeeper Dean Henderson.
Palace pushed for an equaliser and it came when Everton failed to deal with a Tyrick Mitchell cross, with the ball reaching the feet of Mateta who powered his shot over Pickford and into the top of the goal.
Both teams had chances for a late winner but it would not come. Palace’s point puts them eight clear of the bottom three.
Point puts Palace focus back on Europe
There was never really any danger of Palace getting dragged into a relegation fight, with Glasner continually pushing the point that the chance of European glory was their focus for the remainder of the season.
This point should mean they will not slip into a surprise domestic survival scrap before the first European final in their history when they play Rayo Vallecano on 27 May in the Conference League decider.
Yet given they play both Manchester City and Arsenal, the title-chasing sides, Palace could still have a big say on where the Premier League title ends up.
Despite playing as recently as Thursday night, Palace looked the stronger team in the latter stages against Everton.
Both Mateta, who was brought on in the 65th minute, and Sarr were threats, and they came close to winning it when Adam Wharton’s long-range effort struck the post.
The draw stops a run of two defeats on the bounce in the league and, even though they have not won a domestic game since beating Newcastle on 12 April, their energy is on finishing the season with another trophy having lifted the FA Cup last season.
