Everton will be smarting after this, a missed opportunity to create momentum following Monday’s grandstand finish against Arsenal.
Rafa Benitez’s team poured forwards in the closing stages at Selhurst Park after substitute Salomon Rondon scored his first goal for the Club to halve the visitors’ deficit.
Andros Townsend looked poised to equalise but was thwarted by a desperate block. And Vicente Guaita pulled off a tremendous reflex save to frustrate Anthony Gordon, the other player sent on by Benitez as Everton tried to recover from 1-0 down early in the second half.
Moreover, Everton thought they’d not only weathered a Palace storm but gained an attacking foothold in the game when Conor Gallagher made full capital on a mistake to put the hosts in front four minutes before half-time.
James Tomkins converted at a corner on 62 minutes but Everton came roaring back with Rondon’s goal and a sustained period of pressure.
Indeed, there was a giant groan around Selhurst Park when five minutes of stoppage time was added.
But Everton rushed a free-kick close to their own goal and Gallagher swarmed forwards to curl into the top corner and kill the contest.
The away side can legitimately feel a few decisive breaks went against them but there is no real time to dwell on this result, with a visit to Chelsea in the offing.
Guaita in Palace’s goal wasn’t properly extended until 31 minutes had elapsed.
But, fittingly in this part of the country where the buses apparently arrive in pairs following an interminable wait for one, Everton busied the Spaniard twice in quick succession.
Demarai Gray, who had struck an early sighter down the keeper’s throat, skipped forwards following a strong Michael Keane challenge on halfway and forced Guaita into an agile stop down to his left.
Andre Gomes, starting a Premier League match for the first time since 1 May – 225 days ago – was next to take aim.
The legwork was undertaken by Ben Godfrey, evading a challenge from Gallagher and barrelling past Joel Ward before directing the ball into the middle.
Gomes arrived on cue to sidefoot a volley that Guaita had to stand still to hold. Had the ball travelled either side of him, Guaita would likely have been up the proverbial creek.
Palace’s breakthrough four minutes before half-time stung Everton all the more for the visitors, surely, feeling they were beginning to get the measure of their quicksilver hosts.
Benitez’s side will curse the self-inflicted nature of the setback after so much good defensive work, too.
In the build up to the goal, Everton were as solid as in the previous 41 minutes. Godfrey blocked a shot and when the ball was recycled for a cross, Seamus Coleman was stationed to make the clearance.
Jordan Ayew didn’t switch off, though, and was ready to take advantage when Gray underhit a pass steered back towards his own goal.
Off Ayew went, progressing to cut a ball into the middle for Gallagher to sweep-in at the near post.
Ayew was a problem for Everton in the opening 20 minutes or so but prior to his assist – and in common with his team – the Ghanaian was going off the boil.
The Palace forward had the game’s first real opportunity, darting onto a return pass from Odsonne Edouard but denied at close range by the right leg of Jordan Pickford.
Cheikhou Kouyate was urged to shoot by the locals when the ball eventually landed with him 25 yards from goal but the midfielder’s radar was way off.
Everton spent an awful lot of the opening half hour defending. There was a brilliant header from Coleman to prevent Edouard from converting an Ayew cross
Pickford was sharp at his near post to deny Wilfried Zaha – hitherto shackled by Coleman – and the Everton keeper made a more straightforward stop from a Gallagher free-kick on the quarter hour.
Gallagher was providing thrust and pace in Palace’s midfield and an earlier effort on the turn zipped narrowly over the top.
Marc Guehi, up for a corner, saw a low prod squirt wide off Godfrey, who followed his burst to tee-up Gomes with a juddering challenge on Ayew right in front of the audibly impressed Evertonians.
Indeed, this was another good turn from Godfrey at left-back. Even when dispossessed by Gallagher deep in Palace territory, the Everton player recovered to snap into a tackle and stop Joel Ward advancing upfield.
The effervescent Gallagher was exerting a noticeable influence, however. He was wide with a header from Zaha’s left-wing cross five minutes after the restart.
And when the young England player couldn’t gather in a Tyrick Mitchell ball over the top, Keane needed to stay alert to block Edouard’s strike on the follow up.
Gallagher had no such issues controlling Ayew’s scooped pass in the box but seemed to briefly lose his bearings before a weak effort that nevertheless required Pickford to apply a fingertip at his front post.
Pickford then used an outstretched leg to stop Zaha’s cross reaching the advancing Edouard in front of goal.
Benitez sought to turn the tide with the introductions of Rondon and Gordon on 58 minutes, Richarlison and Fabian Delph making way.
But the forward duo had barely had the chance to break sweat than Palace extended their lead.
Will Hughes, on his first Palace start, lifted a corner from the right all the way to the far post.
Only James Tomkins will know if he profited from a slice of fortune to control a ball he saw very late. No doubt the defender knew what he was doing with the second touch, steered into the corner.
Everton persevered and won a free-kick in a promising position when Ward misjudged a tackle on Gray.
The wronged player picked himself up to send the dead ball narrowly over.
But the episode served as notice the game wasn’t dead and two minutes later Everton were back in it.
Rondon’s control with his back to goal in the first instance was superb, the striker collecting Coleman’s lifted pass to feed Abdoulaye Doucoure.
The Frenchman’s low strike deflected off Ward and into the path of Rondon, who toed in his first Everton goal.
And we had to wait only a matter of minutes for Everton to threaten a leveller.
Godfrey was far too strong for Ward, the defender muscling forward to find Rondon for a pass to Townsend.
The equaliser seemed inevitable as Townsend – still very popular here, judging by the pre-kick-off ovation – drew back his right boot.
That was until Jeffrey Schlupp, on as a substitute moments earlier, got a vital touch to divert the shot off target.
The danger from Palace was all on the counter, now – and even then, the home team’s raids doubled as opportunities for Everton to return fire.
Ayew was caught on his heels when substitute Christian Benteke bundled to the byline to centre and following Godfrey’s clearance, Everton sped up the other end.
Guaita, though, made the save of the match, when Gordon executed a big one-two with Townsend to sprint forward and shoot low to the keeper’s right.
Ward reacted in the nick of time to deny Doucoure a go at the rebound.
The metaphorical wind was at Everton’s backs but – against the late run of play – Palace scored the game’s fourth goal, the outstanding Gallagher having the final word with a 20 yarder placed perfectly beyond the blameless Pickford.