A battling 1-0 triumph at bottom club Burnley gave Leicester their fourth consecutive league victory and lifted Nigel Pearson's side into 17th position, one point above the bottom three.
Burnley's Matt Taylor slammed a 59th-minute penalty against the post. The visitors counter-attacked from the rebound and Jamie Vardy tapped the ball in to give his team their fourth straight win in the top-flight for the first time since 1966.
At the other end of the table champions Manchester City leapfrogged Arsenal and Manchester United, who both play home matches on Sunday, with a rollercoaster 3-2 home victory over Aston Villa after the hosts had let slip a two-goal lead.
Runaway leaders Chelsea, who are nine points in front of Manchester City with two games in hand, visit Arsenal on Sunday.
A goalless draw for Liverpool at West Bromwich Albion kept the five-times European champions in fifth place ahead of Tottenham Hotspur and Southampton who shared a 2-2 draw on the south coast as the battle for Europa League qualification intensified.
Liverpool captain Steven Gerrard made his 500th league appearance in his final season in England.
LEICESTER RALLY
Leicester's recent rally represents a remarkable reversal of fortunes. They were bottom for 140 days before climbing two places last week.
No team has avoided relegation having been bottom for that long since the Premier League began 23 years ago but their scintillating form suggests history could be made.
"You've got to find ways of winning games," Pearson told the BBC. "The players have deserved the breaks they've got through a lot of honesty, hard work and ability."
Defeat plunged Burnley deep into the relegation mire, leaving them five points from the safety zone on 26 points with four games remaining.
It was another tale of a missed penalty in the bottom three as Queens Park Rangers remained 19th on 27 points after top scorer Charlie Austin failed to convert a first-half spot kick in a 0-0 home draw with West Ham United.
Sunderland are third from bottom after a 1-1 draw at Stoke City.
The visitors took a first-minute lead through Connor Wickham but were pegged back by a superb drive from Charlie Adam midway through the first half.
DIFFERENT THINGS
Manchester City showed they were not ready to hand over the title just yet with a last-gasp win over Villa although Chelsea will be crowned champions if they triumph at Arsenal and again at Leicester City on Wednesday.
The league's top marksman Sergio Aguero opened the scoring in the third minute with his 21st league goal this season after a miscued kick from Villa keeper Brad Guzan handed him an open goal.
Aleksandar Kolarov's second-half free kick made it 2-0. The visitors fought back with goals from Tom Cleverley and Carlos Sanchez before Fernandinho stabbed home the winner in the 89th minute.
"I was not satisfied with the way we played today but sometimes you need different things to win games," Manchester City manager Manuel Pellegrini told Sky Sports.
"The results are always more important than the performances but I think we normally play well. Today we showed the spirit and the belief that perhaps we have not had in other games when we have had more possession."
Hull City, who are fifth from bottom, won 2-0 at Crystal Palace but remained only one point above the relegation zone while Newcastle United lost 3-2 against Swansea City, their seventh straight league defeat.
(Editing by Ed Osmond and Toby Davis)
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