Leeds United will climb five points clear of the relegation zone if they are able to defeat Crystal Palace at Elland Road on Sunday.
Everton lost 2-0 in the early kick-off against Manchester United, while Nottingham Forest were condemned to a 2-0 defeat at Aston Villa.
The Toffees only remain outside the relegation zone on goal difference, and are tied on 27 points with Nottingham Forest.
READ MORE: Leeds United's best and worse-case relegation battle scenarios this weekend
Leicester City remain two points adrift of safety after Bournemouth prevailed 1-0 at the King Power Stadium. Gary O'Neil's men moved three points clear of the drop-zone with a third win in six Premier League games.
The Cherries sit one place and one point above Leeds after Phillip Billing scored the only goal of the game. Southampton sunk to a third defeat in four as Manchester City eventually coasted to a 4-1 victory at St Mary's after a tight first half.
While Bournemouth leapfrogged Leeds in the table, Wolves and West Ham also moved above Javi Gracia's side with important wins.
Wolves compounded further misery on Chelsea by condemning Frank Lampard to defeat on his second managerial debut for the Blues.
Matheus Nunes scored the only goal just past the half-hour mark with a stunning volley into the far top corner. Julen Lopetegui's climbed into 12th place and four points clear of danger.
West Ham sit one place and one point below Wolves after responding to their 5-1 defeat against Newcastle, with a 1-0 victory over Fulham at Craven Cottage.
Harrison Reed turned Jarrod Bowen's low cross into his own net in the 23rd minute as Fulham extended their winless run to five games in all competitions.
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