Centre-back Robert Huth scored twice, either side of a brilliant Riyad Mahrez goal, as Leicester recorded the finest win of their sensational 12-month rise from bottom to top of the English top flight.
Tottenham Hotspur leapfrogged City into second place by beating Watford 1-0. Arsenal can also move above Manuel Pellegrini's side if they win at Bournemouth on Sunday.
"There are a lot of super teams now. We will try. Why not?" said Leicester manager Claudio Ranieri, whose side visit Arsenal in another top-of-the-table encounter next weekend. "The effort is a lot. Now it is important the players recover because we spent a lot of energy. Sometimes we run more than a bull. We play every match as though it is the last match.
Leicester were bottom of the Premier League a year ago and seemingly destined for relegation, but are now closing in one of the most extraordinary triumphs in English sporting history.
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Huth opened the scoring from a third-minute Mahrez free-kick and headed in Leicester's third goal from a Christian Fuchs corner on the hour after Mahrez had darted through the ragged City defence to make it 2-0.
Sergio Aguero reduced the arrears with a glancing header in the 87th minute -- his seventh goal in five games.
"There are 39 points to play for. Nothing is finished," said Pellegrini, whose side host Tottenham next weekend.
"It is important for us to recover our players and I am continuing not giving up because we got an unexpected defeat, but we must continue."
told the BBC. "We are in a very good position in the league, but the philosophy from the beginning of the season has been to go step by step. We are a very young squad so it is important to keep going and take every game and competition and be ready to compete."
Elsewhere, Adam Johnson and Jermain Defoe scored as second-bottom Sunderland came from 2-0 down to snatch a 2-2 draw at Liverpool, whose manager Jurgen Klopp was absent due to appendicitis.
Despite losing Dejan Lovren and Joe Allen to injury, Liverpool went 2-0 up through Roberto Firmino and Adam Lallana. But Liverpool's fans deserted the stadium in droves in the 77th minute in protest at rising ticket prices and Sunderland fought back, Johnson curling in a free-kick before Defoe equalised in the 89th minute.
Everton leapt three places to eighth, above Liverpool on goal difference, with an impressive 3-0 success at Stoke City.
All of Everton's goals came in the first half, Romelu Lukaku netting an 11th-minute penalty before Seamus Coleman and Aaron Lennon found the net.
Resurgent Southampton closed to within two points of sixth-place West Ham United with a 1-0 home win over Slaven Bilic's side. Maya Yoshida scored a ninth-minute winner for Southampton, who had Victor Wanyama sent off for scything down Dimitri Payet.
Norwich City took their place in the bottom three after losing 2-0 at bottom club Aston Villa, who scored through Joleon Lescott and Gabriel Agbonlahor. Villa are now eight points from safety with 13 matches to play.
Crystal Palace ended a run of five straight defeats with a 1-1 draw at Swansea City, where Gylfi Sigurdsson's 13th-minute free-kick for the hosts was cancelled out by a close-range Scott Dann effort.