Everton had Mason Holgate sent off as they dropped into the Premier League relegation zone despite a battling goalless draw at Crystal Palace.
Sean Dyche's side were forced to hang on for the final 10 minutes at Selhurst Park after Holgate was shown a second yellow card when he tripped Jordan Ayew, earning a point that did little for their survival hopes.
Leicester's victory against Wolves meant that Everton slipped back into the bottom three after as their winless run in the league extended to five games.
The result ended Palace's perfect winning streak under Roy Hodgson who replaced the sacked Patrick Vieira in March, but their top-flight status now looks all but secure.
It was the home team that had the best of the first half. Ayew had a sight of goal after eight minutes, rising to meet Michael Olise's whipped cross before thumping his header over the bar.
Olise then injected excitement into a tepid first half when he burst past Vitalii Mykolenko with muscle and speed down the right, claiming a penalty as he went to ground under the Everton defender's challenge, but referee John Brooks waved it away.
When Palace did muster a shot on target in the 22nd minute, Olise's effort flew straight into Jordan Pickford's grasp.
Palace were in control but it was Everton who had the best moment of the half. Tyrick Mitchell swung a careless leg at Dwight McNeil's cross and the ball dropped onto the right foot of Alex Iwobi, who lashed it back goalwards on the volley. Sam Johnstone dived low and beat it away with two hands as it sped towards the corner.
McNeil had a final stab at giving the first half a goal, he cut in from the left and tried his luck but his drilled effort found only the goalkeeper's gloves.
When Eberechi Eze darted in behind Everton and lifted the ball over Pickford just before the hour mark, Palace thought they had the lead, before celebrations were cut short by the offside flag. VAR checked it, but Eze had made his run fractionally early.
Dominic Calvert-Lewin was inches away from marking his first start since February with a goal. Pickford's huge punt upfield was just barely dealt with by Palace, but no one had picked up Iwobi whose ball into the returning striker was so nearly finished off after an intelligent touch and spin.
Palace's perfect run since Hodgson's return as manager was under threat, though not to nearly the same extent as Everton's Premier League future. It was they who turned up the intensity as the game entered its final quarter, penning the home side in their own half, searching out the goal that would give their survival bid back its lift.
It was against the run of play then that Palace almost took the lead on the break 15 minutes from time. Ayew skipped into the box and cut the ball back to Eze who took a touch, opened up his body and bent a shot towards the bottom corner that Pickford did well to turn behind.
Then came a moment to dash Everton's ambitions. Holgate had already been booked when he lunged at Ayew as the pair raced together down the left. A second yellow was inevitable, and Holgate was dismissed.
Mitchell and Luka Milivojevic had efforts blocked as Everton sat back and clung to their point. Pickford hung gratefully after diving to grab Eze's driven low cross.
Dyche's side saw the game out, but their future looks increasingly uncertain.
