The Foxes, Premier League champions in 2016, are battling to try not to play in that frame of mind without precedent for nine years.
"We missed a punishment for 3-1, yet additionally in the main half we were second best for extensive stretches," Leicester supervisor Dignitary Smith said.
We emerged from the last three, however, there are as yet four games to go."
Everton, who last played in the second level in 1954, stays in the nineteenth spot.
Sean Dyche's side is one point from security with four games left for every one of the last five clubs.
Everton barely got away from assignment last season under Honest Lampard, however, their battles again this term prompted Dyche's arrangement in January.
The Toffees beat Weapons Store and Leeds in two of Dyche's initial three games, yet have won only one of the 11 games from that point forward, igniting angry fan challenges to the club-ordered progression.
I realized being a challenge was going. The main wrongdoing this evening was two truly delicate objectives, however, the attitude is what we need."
In spite of the mutinous state of mind among Everton's voyaging fans, they started to lead the pack in the fifteenth moment.
Timothy Castagne unnecessarily surrendered a punishment with a rash push on Calvert-Lewin as the striker attempted to control Seamus Coleman's flung pass.
Calvert-Lewin crushed the spot-kick into the top of the net for his most memorable objective since October and just his second of a physical issue tormented Crusade.
Leicester required a reaction and they conveyed unequivocally with two objectives over the course of about 11 minutes.
Harvey Barnes' 22nd-minute cross was going back across the objective by Wout Faes and Soyuncu jumped with a half-volley that escaped Jordan Pickford's frail endeavor save.
Vardy rolls back the years
Everton's creaky protection was uncovered again following 33 minutes.
Everton were in disorder at the back and Michael Keane surrendered a punishment in first-half stoppage time when he shut Barnes' cross with his out-extended arm.
Be that as it may, Maddison impacted his punishment directly at Pickford to give Everton reestablished trust.
The save was likewise a recognition of Britain's guardian Pickford's planning.
TV cameras showed a picture of his water bottle toward the rear of the net shrouded in insights regarding potential Leicester punishment takers, including the note: "James Maddison - Remain - 60% focus".
"I got my work done. I called it earlier today about where I would go. He is a decent player and he would've anticipated that I should move however I twofold feigned him," Pickford said.
In a strained finale, Vardy's header was fallen asleep the line by James Tarkowski, while Iversen saved at Calvert-Lewin's feet, then repulsed Abdoulaye Doucoure's rocket.