Against Brighton on Saturday, Carlo Ancelotti's men picked up another three points and moved into 11th place in the Premier League table, level with Arsenal, who are marginally ahead on goal difference.
Richarlison's first-half strike was the difference between the sides at Goodison Park, as the Blues picked up another win under their new boss.
After the match, this is how the national media reacted to the victory.
BBC Sport's Lorraine McKenna thought the Blues were more than worthy winners on the day: the perfect start to getting back on track after last weekend.
She wrote: "Everton produced a dominant display to beat Brighton in the Premier League as they responded well to their humiliating FA Cup defeat by Liverpool last Sunday.
"The Toffees deservedly took the lead after 38 minutes thanks to the superb skill of Brazilian forward Richarlison, who controlled Lucas Digne's pass, swivelled and curled an effort low into the far corner past Brighton goalkeeper Mat Ryan.
"While there were some boos from sections of the crowd when Delph came on for the impressive Bernard on 71 minutes, that was the only real sour note for the home side."
In the Daily Mail , Derek Hunter also focused on the long road that Ancelotti must traverse if he is to achieve his Everton goals, once more making clear that while there is still a long way to go, this was an excellent response.
He wrote: "Carlo Ancelotti is all too aware that forgiveness will be a long process. Beating Brighton was never going to be enough to regain the trust of Everton’s supporters. It was, though, a start.
" A feeble FA Cup exit to an under-strength Liverpool last weekend was too much to bear for fans sick of waiting for trophies while watching their neighbours run away with the Premier League.
"The very least they expected in response was a performance of commitment. They got one but the victory it secured was not as straightforward as it should have been.
"For a while it looked as if Everton might win comfortably. They began with purpose, should have had a penalty and were in front by half-time with a superbly taken goal from Richarlison.
"The manager is not one to be thrown by such discord but Ancelotti understands the anger in the stands. There is damage to be repaired and it will take time."
The Guardian's Paul Wilson was realistic about the level of the performance, which can still be vastly improved, though he pointed out that the win was certainly needed.
He explained: "This was not quite the crowd-pleasing performance Ancelotti will have been hoping for as his Everton side attempted to draw a line under the nightmare that was Anfield.
"At least it was a second home win for the new manager and another three points to add up to a reasonable haul of nine from four games in charge.
"While Ancelotti will have been pleased that the home crowd got behind the players after some expressions of discontent in midweek, he will be aware that the mood might easily have shifted had Brighton grabbed a draw with one of a couple of late chances."
Everton face West Ham United at the London Stadium next weekend as they look to build on this three points.
