EPL Table: 2018 Standings After Saturday's Week 36 Results and Top Scorers

Chelsea's hopes of finishing in the top four remain alive after a 1-0 win over Swansea City on Saturday that keeps Carlos Carvalhal's side in trouble at the bottom of the table.

The Swans are just a point off the relegation zone and will be looking nervously over their shoulders after all the teams in the bottom three picked up points on Saturday.

Bottom side West Bromwich Albion kept their slim hopes of survival alive with victory at Newcastle United, while Stoke City drew 0-0 at Liverpool and Southampton beat Bournemouth 2-1.

Here's a look at all Saturday's results, the updated table, Premier League top scorers and a recap of the day's action.

Saturday's Results

Liverpool 0-0 Stoke City

Burnley 0-0 Brighton & Hove Albion

Crystal Palace 5-0 Leicester City

Huddersfield Town 0-2 Everton

Newcastle United 0-1 West Bromwich Albion

Southampton 2-1 Bournemouth

Swansea City 0-1 Chelsea

Premier League Table (games played, goal difference, points)

1. Manchester City: 34, +73, 90

2. Manchester United: 34, +39, 74

3. Liverpool: 36, +43, 72

4. Tottenham Hotspur: 34, +35, 68

5. Chelsea: 35, +26, 66

6. Arsenal: 34, +20, 57

7. Burnley: 36, +3, 54

8. Everton: 36, -12, 48

9. Leicester City: 35, -3, 44

10. Newcastle United: 35, -9, 41

11. Crystal Palace: 36, -13, 38

12. Bournemouth: 36, -18, 38

13. Watford: 35, -18, 38

14. Brighton & Hove Albion: 35, -15, 37

15. West Ham United: 34, -21, 35

16. Huddersfield Town: 35, -29, 35

17. Swansea City: 35, -25, 33

18. Southampton: 35, -19, 32

19. Stoke City: 36, -33, 30

20. West Bromwich Albion: 36, -24, 28    

Premier League Top Scorers

Mohamed Salah, Liverpool, 31 goals

Harry Kane, Tottenham, 26 goals

Sergio Aguero, Manchester City, 21 goals

Raheem Sterling, Manchester City, 18 goals

Jamie Vardy, Leicester City, 17 goals

Romelu Lukaku, Manchester United, 16 goals

Roberto Firmino, Liverpool, 15 goals

Saturday Recap

Chelsea scored after just four minutes at the Liberty Stadium when Eden Hazard found Cesc Fabregas and he curled a fine shot past goalkeeper Lukasz Fabianski.

Opta noted how it was Fabregas' 50th Premier League goal:

The Blues were the better team in the first half but could not add to their tally, and Swansea improved after the break.

However, both teams found clear chances hard to come by, and Swansea's best opportunities were shots on goal from Alfie Mawson and Wayne Routledge that failed to trouble Thibaut Courtois.

The win sees Chelsea close the gap to Tottenham Hotspur in fourth to just two points and boosts their hopes of securing UEFA Champions League football for next season.

Swansea are just a point above the relegation zone and still have work to do in their remaining three Premier League games to preserve their Premier League status.

Earlier in the day. Liverpool could not replicate Tuesday's UEFA Champions League heroics, failing to break down a committed Stoke side at Anfield.

Premier League top scorer Mohamed Salah had a brilliant chance to open the scoring when he was sent clean through on five minutes, but he put his effort wide of Jack Butland's goal. 

James Pearce at the Liverpool Echo noted how rare it was for the Egyptian not to score:

Stoke also had chances: Mame Biram Diouf headed into the side-netting, and a sliding Peter Crouch could not quite convert Xherdan Shaqiri's cross.

Liverpool were the more wasteful side, though. Georginio Wijnaldum fired into the side-netting and Danny Ings saw a strike correctly ruled out for offside.

There was controversy late on too when the Reds were denied a penalty after Wijnaldum's cross struck Erik Pieters' arm.

It was a subdued performance from Liverpool, who lacked their usual precision in the final third. However, it's a precious point for Stoke, who rode their luck at times but will retain belief they can beat the drop.

Crystal Palace were Saturday's biggest winners. They hit five past Leicester City to move into 11th place in the table and all but ensure their Premier League safety.

Manager Roy Hodgson said he thinks his side will now stay up, per Gary Taphouse at Sky Sports:

Wilfried Zaha sent Palace on their way with a fierce strike for the opener before James McArthur added a second on 37 minutes.

Leicester had Marc Albrighton sent off 10 minutes into the second half for pulling down Zaha, and the visitors crumbled afterwards.

Palace scored three times in the final 10 minutes, with Ruben Loftus-Cheek, Patrick van Aanholt and Christian Benteke all on the scoresheet to seal an emphatic win.

West Brom continued their fine form under caretaker manager Darren Moore with a narrow victory at St James' Park. 

Matt Phillips smashed home the only goal of the game on 28 minutes after a pass from Jake Livermore. Newcastle did have chances, but goalkeeper Ben Foster made a great save from Dwight Gayle and Kenedy hit a post.

Football correspondent Craig Hope showed how Moore's record compares to previous manager Alan Pardew's:

It still looks as though it will be too little, too late for West Brom, but Moore has done a superb job to turn the team's fortunes around and will have given the team hope they can bounce straight back.

Southampton will also be optimistic they can stay up after a first Premier League victory under Mark Hughes. Dusan Tadic scored twice for the Saints, who move to within a point of Swansea and safety.

Hughes' side face Everton next and then head to the Liberty Stadium in a game that will have a huge bearing on the relegation race.