Bangladesh Time: Jamie Vardy grabbed the only goal of the game on the hour-mark just seconds after Matt Taylor had missed a golden chance to put the hosts ahead from the penalty spot.
Leicester had to survive a late onslaught from the home side and only a stunning stop from Kasper Schmeichel - who beat out a deflection off Robert Huth - preserved their advantage.
And Hull improved their survival chances with a deserved 2-0 victory over Crystal Palace at Selhurst Park. Dame N'Doye (51 and 90) ensuring all three points returned to Humberside.
Sunderland's hopes of maintaining their top-flight status, looking more precarious by the week, suffered another blow as they were held to a 1-1 draw by Stoke at the Britannia Stadium.
Connor Wickham gave them the perfect start with a goal in the first minute but they ended the day in the bottom three after Charlie Adam pounced shortly before the half-hour mark.
Queens Park Rangers remain firmly in the drop zone after they were held to a goalless draw by West Ham United at Loftus Road.
Charlie Austin had the ideal opportunity to claim all three points but he hit the post with a 21st-minute penalty.
Newcastle's miserable season goes from bad to worse after they suffered their seventh successive defeat, 3-2 at the hands of Garry Monk's Swansea at St James' Park.
Ayoze Perez (20) fired the Magpies in front but Nelson Oliveira (45) levelled on the stroke of half time before second-half goals from Gylfi Sigurdsson and Jack Cork prompted a mass exodus from the home stands. Siem De Jong, playing his first game for Newcastle since last August, grabbed an 87th-minute consolation for John Carver's side.
In a largely uneventful game at the Hawthorns, West Bromwich Albion and Liverpool ended goalless.
Earlier, Tottenham twice came from behind to earn a draw at fellow-European hopefuls Southampton at St Mary's.
Goals in either half by Saints striker Graziano Pelle (29, 65) were cancelled out by Erik Lamela (43) and Nacer Chadli (70) to earn Spurs boss Mauricio Pochettino a share of the spoils on his return to the south coast.
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