EVERTON 4-2 LEICESTER Davies (1' minutes), R Lukaku (23' minutes, 57' minutes), Jagielka (41' minutes)
Slimani (4' minutes), Albrighton (10' minutes)Everton moved within goal difference of Arsenal in sixth as Romelu Lukaku scored twice to check Leicester's renaissance under boss Craig Shakespeare.
Tom Davies poked in for the hosts after 30 seconds, before Leicester rallied with a slick counter-attacking goal from Islam Slimani and a superb free-kick from Marc Albrighton.
But Leicester, much changed before Wednesday's Champions League quarter-final at Atletico Madrid, never looked comfortable.
Lukaku headed in a Ross Barkley cross to draw Everton level and Phil Jagielka was allowed too much space at a corner as the Toffees reached the break ahead.
Lukaku drilled in from close range after the interval and the withdrawal of the bright Demarai Gray and striker Jamie Vardy seemed to signal Leicester's attentions turning towards Europe.
Marc Albrighton speaking to Sky Sports:
"We were sloppy. I wouldn't say they've carved us open for any amounts of the game. The goals we gave away were cheap and not good enough. When you need to score five goals away from home it's always going to be difficult.
"Don't get me wrong, the run we've been on in the last six weeks has been absolutely fantastic and the application the boys have shown has been tremendous. You can't afford slip-ups and Everton proved that today."
[On if he meant his free-kick to go in] "Yep. You put a ball in an area and when you're on free-kicks you aim for the back post, that's what you're taught at a young age and luckily it went in."
[On Wednesday's Champions League game against Atletico Madrid] "We're big enough to know we have to dust ourselves down and we're all excited for Wednesday night and it's going to be a great occasion but we have to improve on that performance today."
Everton striker Romelu Lukaku on Sky Sports: "We did really well. In away games we have to do the same.
"We want to fight against (fifth place) Manchester United and (sixth place) Arsenal. We need to win much more games.
"Myself and Ross [Barkley] have played together many times. In his new position he can create more. Hopefully we can deliver more in the upcoming games."
Everton's Ross Barkley speaking to Sky Sports:
"It was entertaining today.The big man [Lukaku] was on fire today and we got the three points which was the main thing. We thought we desereved the three points midweek against United which was disappointing. We stuck at it today and we knew we had a lot of players in top form at the minute.
"I'm just enjoying it at the minute getting the chance to get in the box and create chances like I did today."
[On criticism after the Merseyside derby] "It's to be expected it's the Merseyside derby and we expect more from ourselves in big games.
We went away and worked hard and put a shift in midweek and got the three points today which is the main thing."