Everton moved out of the Premier League relegation zone with a ruthless 5-1 win at Brighton on Monday, while Leicester's hopes of survival are hanging by a thread after a 5-3 defeat at Fulham.
Nottingham Forest also pulled themselves clear of the bottom three as they beat fellow strugglers Southampton 4-3.
Brighton are in the hunt to qualify for Europe for the first time in the club's history, but a heavy schedule appeared to have taken its toll on Roberto De Zerbi's men as they were torn apart by an Everton side that had not won away since October.
The Toffees had the dream start as Abdoulaye Doucoure opened the scoring after just 34 seconds.
Doucoure's brilliant volley from Dwight McNeil's cross doubled Everton's lead before Brighton goalkeeper Jason Steele deflected McNeil's cross into his own net.
De Zerbi responded by making four half-time substitutions and Brighton peppered the Everton goal but were caught out on the counter-attack when McNeil showed great poise to round Steele to make it 4-0.
Alexis Mac Allister pulled a goal back after Kaoru Mitoma's initial effort came off the post.
But McNeil had the final say as he rounded off a dazzling performance by smashing into the top corner in stoppage time.
A first win in eight games lifts Sean Dyche's men two points clear of the drop zone.
"It's a quality of performance that we want to build," Dyche said. "It shows it is in there - it's the consistency I've been searching for."
Brighton remain in seventh, two points behind Tottenham with two games in hand, but their outside shot at a top-four finish appears gone.
- Leicester's mental struggles -
Leicester boss Dean Smith admitted his players are struggling with the pressures of a relegation battle after a disastrous defensive display at Craven Cottage.
The Foxes, who won the Premier League in stunning fashion in 2016 and lifted the FA Cup two years ago, are staring relegation in the face.
Victories for Everton and Forest pushed Leicester into the relegation zone and they also face a tough run-in with Champions League-chasing Liverpool and Newcastle to come before ending the season at home to West Ham.
Only Leeds and Bournemouth have conceded more goals than Leicester in the Premier League and defensive deficiencies were again their undoing at Craven Cottage.
Goals from Willian, Carlos Vinicius and Tom Cairney put Fulham 3-0 up before half-time.
"The first-half is what killed us," said Smith. "You can't give three-goal leads at this level and expect to come back."
"Some of them are struggling mentally with the pressures, but that's for me and the coaching staff to sort out and pick the right team."
Cairney and Willian struck again either side of Harvey Barnes' consolation goal to make it 5-1.
Jamie Vardy also saw Leicester's first penalty of the game saved by Bernd Leno in an action-packed second-half before the visitors pulled two more goals back in the final 10 minutes.
James Maddison converted a second penalty before Barnes pounced to make it 5-3 after a calamitous defensive mix-up between Shane Duffy and Leno.
Forest moved three points clear of the drop zone in a seven-goal thriller that virtually sealed Southampton's fate.
"There was so much that went on in the game," said Forest boss Steve Cooper. "I am really pleased with some of the quality we showed in attack, creating chances and scoring, but we didn't cover ourselves in glory with the goals we conceded."
Two goals in three minutes from Taiwo Awoniyi put Forest on the road to victory before Carlos Alcaraz pulled a goal back.
Morgan Gibbs-White restored the hosts' two-goal lead from the penalty spot, but they had to survive some nervy moments after Lyanco's header made it 3-2 early in the second half.
Danilo rounded off a fine team move 17 minutes from time to give Cooper's men breathing space at the bottom despite James Ward-Prowse's penalty in stoppage time cutting the arrears once more.
Southampton are eight points from safety with three games remaining.
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