Everton moved up to seventh and within five points of the Premier League top four as their resurgence under Carlo Ancelotti continued with a 3-1 win over Crystal Palace on Saturday.
Bernard, Richarlison and Dominic Calvert-Lewin scored the goals for the Toffees, who have won five and drawn two of eight league games since the Italian took charge in December.
"Since I arrived the team did a fantastic job," Ancelotti told BT Sport. "Now we have a possibility to think about Europa League."
At the other end of the table, Palace are looking over their shoulders at the relegation zone.
Roy Hodgson's men still have a six-point lead over the bottom three, but have not won in eight games and just once in the league since early December.
"I can't fault the players' effort, but it's another defeat and another we go home without points," said Hodgson.
"We know what we have to do. When we moved the ball quickly we asked questions and were close to getting more than one goal."
Bernard gave the hosts a deserved first half lead with a thumping finish from Theo Walcott's cross to the back post.
However, Palace were gifted a route back into the game six minutes into the second half thanks to another error from Everton goalkeeper Jordan Pickford.
The England number one's place at Euro 2020 is under debate and he let Christian Benteke's shot slip underneath his body as the Belgian striker registered his first goal of the season.
"Disgusting. I was disappointed with myself," said Pickford, who later made amends with a fine save to preserve Everton's 2-1 lead.
"My studs got caught but I hold my hands up for that. I reset and I never let anything affect me."
Just as Everton were wobbling, though, a moment of magic from Richarlison swung the game back in their favour seven minutes later.
The Brazilian stormed onto Calvert-Lewin's flick-on to carry the ball from just inside the Palace half and past Gary Cahill before placing his shot into the far corner.
"Richarlison did a fantastic counter attack and we won for this reason," added Ancelotti. "He is a fantastic player in counter attack, he used that situation really well."
The same two players were involved when Everton sealed the points two minutes from time as Richarlison's header from a corner came off the bar and Calvert-Lewin turned home his 13th goal of the season.
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