Everton's Alex Iwobi rescued a 2-2 draw against relegation rivals Leicester, but it was the Foxes who climbed out of the Premier League's bottom three after Monday's pivotal showdown.
Iwobi scored a second-half equaliser at the King Power Stadium after James Maddison wasted a chance to put Leicester 3-1 up when his penalty was saved by Jordan Pickford.
Dominic Calvert-Lewin put Everton in front with an early penalty, before Leicester hit back with goals from Caglar Soyuncu and Jamie Vardy.
Leicester, who have won one of their last 12 league games, moved out of the relegation zone on goal difference.
The Foxes, Premier League champions in 2016, are fighting to avoid playing in the Championship for the first time in nine years.
"We missed a penalty for 3-1, but also in the first half we were second best for long periods," Leicester boss Dean Smith said.
"We knew the result today would not define what happens. We came out of the bottom three, but there are still four games to go."
Everton, who last played in the second tier in 1954, remain in 19th place.
Sean Dyche's side are one point from safety with four games left for each of the bottom five clubs.
Everton narrowly escaped relegation last season under Frank Lampard, but their struggles again this term led to Dyche's appointment in January.
The Toffees beat Arsenal and Leeds in two of Dyche's first three games, but have won just one of the 11 games since then, sparking furious fan protests against the club hierarchy.
"We held our nerve, kept trying to create things and overall it's a good performance, although we didn't get the three points," Dyche said.
"I didn't come here for a walk in the part. I knew it was going to be a challenge. The only crime tonight was two really soft goals, but the mentality is what we want."
Despite the mutinous mood among Everton's travelling fans, they took the lead in the 15th minute.
Timothy Castagne needlessly conceded a penalty with a rash shove on Calvert-Lewin as the striker tried to control Seamus Coleman's lofted pass.
Calvert-Lewin smashed the spot-kick into the roof of the net for his first goal since October and only his second of an injury-plagued campaign.
Leicester needed a response and they delivered emphatically with two goals in the space of 11 minutes.
Harvey Barnes' 22nd-minute cross was headed back across goal by Wout Faes and Soyuncu pounced with a half-volley that eluded Jordan Pickford's weak attempted save.
Everton's creaky defence was exposed again after 33 minutes.
Iwobi lost possession too easily and Vardy rolled back the years with a blistering run to reach Maddison's pass and round Pickford for a cool finish.
Everton were in disarray at the back and Michael Keane conceded a penalty in first-half stoppage time when he blocked Barnes' cross with his out-stretched arm.
But Maddison blasted his penalty straight at Pickford to give Everton renewed hope.
The save was also a tribute to England keeper Pickford's preparation.
Television cameras showed an image of his water bottle in the back of the net covered in details about potential Leicester penalty takers, including the note: "James Maddison – Stay – 60 percent centre".
"I did my homework. I called it this morning where I would go. He is a good player and he would've expected me to move but I double-bluffed him," Pickford said.
Iwobi made Maddison pay for his miss as the Everton midfielder equalised in the 54th minute, drilling a fine finish past Iversen from 10 yards after Calvert-Lewin flicked on McNeil's cross.
In a tense finale, Vardy's header was nodded off the line by James Tarkowski, while Iversen saved at Calvert-Lewin's feet, then repelled Abdoulaye Doucoure's rocket. (AFP)