A precious victory for Sam Allardyce could not mask the anger that has fermented here over Everton’s miserable season. His team were three goals up and cruising to a second successive home win when Morgan Schneiderlin trotted on as an 80th-minute substitute for the injured Idrissa Gueye. The home crowd greeted him with a chorus of boos.

It was a horrible, chilling reception for the £20m midfielder who, in the week since the 5-1 capitulation at Arsenal and previously, has come to symbolise the expensive transfer mistakes and perceived lack of commitment that has scarred Everton’s campaign. Crystal Palace were soundly beaten for the third time in 16 league games and stand two points clear of the relegation zone but showed a unity that is conspicuous by its absence at Everton.

“I was surprised, very surprised,” said Allardyce of Schneiderlin’s treatment. “I’ve not heard that before. Morgan is a very important part of our squad this year. A lot of players haven’t performed up to their potential, we know that, but they are doing it at home. I can’t ask for more from them at home but away from home it has been a problem.”

Despite animosity and anaemic performances Everton are now two points behind Burnley in seventh after Gylfi Sigurdsson and Oumar Niasse, both striking early in the second half, plus Tom Davies sealed an ultimately comfortable win.

Roy Hodgson finally got an apology from his successor as England manager for mocking his speech 17 months ago. His injury-plagued side could have got a result too but poor defending after the restart undermined an otherwise committed approach.

Hodgson said: “Sam called me on Thursday and apologised. I was happy to receive and accept that apology and, as far as I’m concerned now, that matter belongs in the distant past and I have nothing more to say on the subject. I certainly have no issues with it.”

Everton held the edge throughout with Theo Walcott again impressing on the right and Wayne Rooney’s intelligent distribution standing out in central midfield, although they rarely tested Wayne Hennessey in the Palace goal in the first half.

Fifty seconds after the restart, however, their productivity turned on a touch of good fortune. A long clearance by Jordan Pickford was headed skywards by James Tomkins and Niasse turned the second ball onto Sigurdsson. The Iceland international cut across Timothy Fosu-Mensah and though his low shot was on target it deflected off Tomkins and sailed out of Hennessey’s reach and into the bottom corner.

Gylfi Sigurdsson leads Everton celebrations. Photograph: Mark Robinson/Getty Images

Five minutes later Niasse doubled Everton’s advantage as the Palace defence switched off. Davies released Cuco Martina on the left of the penalty area and the full-back floated a perfect delivery for the unmarked Senegal forward to head home.

To their credit Palace responded well and created two excellent chances to haul themselves back into the contest. The first, a Christian Benteke header from a glorious Yohan Cabaye cross, was steered wastefully wide. The second, an Alexander Sørloth header, was foiled by a fine save from Pickford. Big moments.

Davies ensured there would be no comeback with his first goal of the season. Hennessey scrambled clear when Niasse’s shot was deflected goalwards but only as far as Sigurdsson who clipped the ball back from the byline for the young midfielder to convert from close range.

Luka Milivojevic denied Pickford the clean sheet his performance merited from the penalty spot after Ashley Williams handled late on but Everton’s victory will be remembered for another reason. Schneiderlin was first down the tunnel on the final whistle. Unsurprisingly, he did not stop to applaud.