Jordan Ayew’s brilliant goal gave new Crystal Palace manager Oliver Glasner something to smile about before Amadou Onana’s late header rescued Everton and helped them climb out of the relegation zone.
Ayew’s moment of quality midway through the second half was out of keeping with the rest of the mundanity served up by two struggling teams and made Glasner shine in the directors’ box as he made a brief observation.
But the gloom at Goodison Park dissipated six minutes from time when Palace’s excellent goalkeeper Sam Johnstone missed his strike at Dwight McNeil’s corner and substitute Onana could not miss from just a few yards out.
It had been a busy day for Palace even before kick-off, with Odgson resigning as manager and Austrian Glasner announced as his successor, although coaches Paddy McCarthy and Ray Lewington took charge at Goodison.
On the field it was difficult to determine which team needed the points more.
Amadou Onana’s final header rescued Everton from the relegation fight against Crystal Palace
Dwight McNeil’s corner was headed in from close range by substitute Onana in the 84th minute.
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Everton started in the bottom three and were on the longest winless streak in the Premier League (seven games) as they wait to see if their appeal against a 10-point deduction is successful.
Palace, meanwhile, had won just three of 19 in all competitions and were again without Michael Olise, Eberichi Eze and Marc Guehi, arguably their three best players.
Blues manager Sean Dyche was able to name the influential Abdoulaye Doucoure for the first time in five weeks following a hamstring injury.
The most significant of Palace’s four changes saw one England goalkeeper, Johnstone, replacing another, Dean Henderson, and the team moved to a back three in front of him.
Glasner was on Merseyside to see his new charges, sitting with his new chairman Steve Parrish and Eagles playing legend Mark Bright.
Palace started cautiously but Glasner would have been encouraged to see them break effectively to register Odsonne Edouard’s first-time effort which an alert Jordan Pickford was able to save the first time.
Everton responded with an instant shot from Doucoure that went wide of Johnstone’s post before the goalkeeper began to move.
Only Burnley and Sheffield United have scored fewer goals than the exposed teams, so it was never likely to be an exciting affair.
Dwight McNeil’s cross to Dominic Calvert-Lewin saw the centre-forward’s header nearly end his 18-game drought.
McCarthy had revealed in a pre-match television interview that he had not spoken to Glasner before the match and that the players wanted to commemorate Hodgson’s departure with a performance that he would be proud of.
He would have enjoyed the clever pass through the lines that created a chance for Jefferson Lerma after 35 minutes, but not the shot that sailed over the bar.
Twenty-year-old Adam Wharton, the last major signing of the Hodgson era, looked tidy in midfield, as well as taking set pieces and playing the occasional clever ball.
Jordan Ayew put the visitors ahead with a sensational goal in the 66th minute
The Ghanaian striker unleashed a magnificent shot into the far corner of goalkeeper Jordan Pickford.
He was involved in the best chance of the first half, when Ashley Young cleared Jean-Philippe Mateta’s header off the line.
Hodgson had been criticized for taking out Eze during Palace’s last visit to Goodison when they were knocked out of the FA Cup.
When Paul Tierney whistled for half-time on this occasion, the reaction of both groups of fans was silent, waiting for more excitement.
Traveling Palace fans carried a couple of banners thanking Hodgson for his work during two spells at Selhurst Park, but the lack of attacking force in their side indicated why many thought it was time for a change.
The Evertonians who booed their team at half-time were equally frustrated that their team failed to get a shot on goal in the first 45 minutes.
At least the locals started the second half with more enthusiasm. James Garner ventured forward, but his attempt to reach the top corner was a little ambitious and he headed into the crowd.
No goalkeeper has kept more clean sheets than Pickford despite Everton’s poor position and he ran smartly to block Tyrick Mitchell after Mateta had played full-back.
Edouard let out a little “Ooh” when he attempted a shot from above but unfortunately the ball was more vertical than towards the net.
Idrissa Gueye was the hardest hit by Gwladys Street, irritated by her team’s lack of creativity.
Then, like London buses, Everton recorded their first attempts on goal in quick succession.
Ben Godfrey’s header from a corner went towards the goal until Johnstone saved it. When the rebound fell into Doucoure’s hands, Daniel Muñoz superbly cleared his sideline from near the line.
The home fans got their wish when Gueye was replaced, but the play bounced badly when Palace scored on their next attack.
A long clearance from Johnstone was sent to Mateta, who showed admirable strength to release Ayew just outside the box.
Dominic Calvert-Lewin wasted a great opportunity when he shot over the bar.
Palace striker Jean-Philippe Mateta tangles with Everton defender James Tarkowski
New Crystal Palace boss Oliver Glasner was in the stands at Goodison Park on Monday night.
Unlike the rest of the match, the Ghanaian showed great quality by letting fly and leaving Pickford trapped in the air as the ball raced towards the top corner.
Everton’s desperation to achieve an equalizer led them to lead for the first time in the last 10 minutes. James Garner was denied by a diving Johnstone, but the home team’s aptitude at set pieces finally paid off.
McNeil’s shot in a crowded area was diabolical and after Johnson failed to clear, Onana at the far post scored his third goal of the season.
A point each gave both sides something to cling to, but both Dyche and now Oliver Glasner know that big improvements are needed. For Hodgson, it will probably be a relief to be stress-free.