Leeds United remain two points clear of danger after defeats for Everton, Leicester City and Southampton respectively on Saturday.
Fulham condemned Everton to a 3-1 defeat at Goodison Park with Leeds loanee Dan James scoring his first goal for the Cottagers
Harrison Reed opened the scoring inside 22 minutes, only for Dwight McNeil to equalise 10 minutes before the break. Harry Wilson restored Fulham's lead within six minutes of the restart, and James secured all three points in the 68th minute.
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Southampton remain rock bottom in the Premier League and four points adrift of safety after losing 2-0 at home to Crystal Palace.
Eberechi Eze scored both goals for the Eagles as they climbed nine points clear of the bottom three with a third win on the spin.
Leicester stay in 19th place, and four points behind Leeds after losing 3-1 against reigning champions Manchester City. Erling Haaland scored twice to equal Mohamed Salah's record for most goals in a 38-game Premier League season, while John Stones scored the opener.
Kelechi Iheanacho reduced the deficit 15 minutes from time but Dean Smith started his tenure as interim manager with a defeat. The Foxes have lost four games on the bounce in the Premier League, and are winless in 10 across all competitions.
Leeds cannot drop into the relegation zone this weekend but could slip to 17th if Nottingham Forest spring a surprise by beating Manchester United at the City Ground on Sunday.
Forest are winless in nine league games, and have lost four of their last five, with their recent run of form seeing them plummet into the drop zone.
Elsewhere, Dango Ouattara scored his first Premier League goal in the 95th minute to secure a 3-2 victory at Tottenham Hotspur.
Son broke the deadlock in the 14th minute for Tottenham, before goals from Matias Vina and Dominic Solanke either side of half-time propelled the Cherries into the lead.
Arnaut Danjuma equalised against his former club with two minutes of regulation time remaining, but Ouattara's decisive strike helped guide Bournemouth six points clear of the relegation zone.
Wolves registered back-to-back wins by defeating Brentford 2-0 at Molineux. Diego Costa scored his first goal for the Black and Gold inside the opening half an hour, and Hwang Hee-chan doubled their lead in the 69th minute.
Julen Lopetegui's charges climbed seven points clear of the bottom three, and only sit five points behind Chelsea having played the same amount of games.
West Ham welcome Premier League leaders Arsenal to the London Stadium on Sunday afternoon. The Hammers have collected two wins from three league matches, and boast a game in hand over Leeds, with a three-point cushion separating them from the drop zone.
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