West Ham’s hopes of finishing fourth in the Premier League further diminished with a 2-0 loss at Brentford on Sunday.
After Arsenal lost to Brighton, Tottenham took charge of the race to book a Champions League place after beating Aston Villa 4-0 on Saturday.
West Ham, who could yet reach the Champions League via the Europa League and drew with Lyon in their quarter-final first leg on Thursday, now face an uphill battle to trouble Spurs.
The Hammers lost Kurt Zouma to injury in the first half, and soon after the break Bryan Mbeumo gave Brentford a deserved lead after some lovely build-up.
Just after the hour-mark it was 2-0, with another fine move finished off by Ivan Toney, who headed in for his 12th of the season.
The win lifts Brentford into 13th and takes them one step closer to securing survival, while West Ham remain sixth, six points behind Spurs who have played a game less.
The gap between Brentford and the drop-zone extended to 12 points after 18th-placed Burnley lost 2-0 at Norwich City in another 2pm kick-off on Sunday.
Burnley had been boosted by their midweek win over Everton, but now sit four points behind the 17th-placed Toffees, who beat Manchester United on Saturday.
Norwich are rock bottom but enhanced their own slim chances thanks to goals from Pierre Lees-Melou and Teemu Pukki in either half.
Between the strikes, Maxwel Cornet missed a glorious opportunity to equalise for Burnley, but could only shin his effort wide.
Leicester were clinical and led 2-0 at half-time after goals from Ademola Lookman and Kiernan Dewsbury-Hall.
After the break, Wilfried Zaha saw his penalty saved by Kasper Schmeichel, and after a re-take was ordered and the same outcome occurred, the Palace forward scored the rebound.
Leicester still have games in hand over the teams above them, but a push for the European places would require a near perfect run-in, while the Foxes still harbour hopes of winning the Conference League after drawing their quarter-final home leg 0-0 with PSV on Thursday.