Manager Carlo Ancelotti revealed they have devised a gameplan which now has the Brazil international mainly playing as an out-and-out centre-forward in a 4-4-2 alongside Dominic Calvert-Lewin and they both scored in the 3-1 win over Crystal Palace.
Richarlison occasionally reverts to the left-sided role which he occupied under former manager Marco Silva but, wherever he plays, Ancelotti does not want him to be concerned too about tracking back.
"Richarlison can also play on the left but we don't have to give him a lot of defensive work," said the Italian after the Brazilian scored a brilliant and decisive individual goal to take his Premier League tally to nine this season.
"He has to be fresh when we have the ball, he can play right and left, but without thinking too much about defensive work.
"We have to thank Richarlison because he scored a fantastic goal on the counter-attack. That was the key point and, after, our control of the game was good.
"It was an outstanding counter-attack, he is a fantastic player, really young and really important for us. It was an outstanding goal."
There was no doubting the quality of the goal the Brazilian scored with the game level at 1-1 after Jordan Pickford's error allowed Christian Benteke's first goal since April to cancel out Bernard's first-half volley.
Receiving a flick-on from his strike partner he ran at the rapidly retreating Gary Cahill and, with a number of Palace players racing to cover but not getting near him, he fired a precise shot across Vincente Guaita.
It was a crucial goal as Everton had been under danger of cracking in the 10 minutes after conceding the equaliser.
The roles were then reversed with two minutes to go when Richarlison's header rebounded back off the crossbar for Calvert-Lewin to poke home his 11th league goal of the campaign.
"Strikers scoring goals is important, they need the support from the other players – in some parts of the game we did well and in others we can do better," added Ancelotti, who admitted he was not happy with the opening hour of the game which saw winger Theo Walcott forced off with a knee injury that will require a scan on Sunday.
Victory made it 17 points from Ancelotti's eight matches in charge and lifted a side in the relegation zone two months ago to within five points of the top four.
Palace, however, are on the slide with no wins and just four points from their last seven matches and their problems up front – they are the top-flight's lowest scorers with 23 goals from 25 matches – are hurting them.
"Our goal difference is still a lot better than many of the teams around us," said manager Roy Hodgson, trying to remain positive.
"You have seen the team play and the amount of opportunities they created. If we can continue to do that, I am sure the goals will come."