Updated at 8.45pm with late game
Swansea climbed out of the relegation zone and left Hull back in the bottom three after a 1-0 win over Everton at the Liberty Stadium.
Fernando Llorente's towering header put the Swans in front on 28 minutes.
Despite a second-half recovery from Everton, who still hope to finish in the top six, it was the home side who held on to secure what may well be a crucial victory in their battle to stay in the Premier League.
Swansea moved onto 35 points and up to 17th, one ahead of Hull heading into the final two matches of the campaign.
Earlier, the survival battle had taken another dramatic twist when Hull suffered a shock 2-0 home defeat against bottom club Sunderland.
The Tigers were made to pay for failing to beat inspired Black Cats keeper Jordan Pickford when defender Billy Jones headed in from a corner after 69 minutes.
Pickford produced another good save to deny Abel Hernandez before Hull saw a penalty appeal turned away when Harry Maguire went down.
Jermain Defoe knocked in a second during stoppage time - albeit from an offside position - as Sunderland, relegated last weekend, closed out an unexpected victory which could yet prove pivotal in deciding which team joins them in the Championship next season.
In Saturday's early Premier League game, Manchester City thrashed Crystal Palace 5-0 at the Etihad Stadium to keep themselves on course to finish in the top four.
David Silva set City on their way to what could prove to be three crucial points in the race for Champions League qualification with the opening goal after just two minutes of the lunchtime kick-off.
Palace, who still need to mathematically secure their top-flight status, held out until the start of the second half when captain Vincent Kompany finally doubled City's lead after 49 minutes.
Belgian playmaker Kevin De Bruyne swept in a third just before the hour, with Raheem Sterling adding a fourth goal with eight minutes left before a late header from Nicolas Otamendi completed the rout.
City move above Liverpool on goal difference, having now played the same number of games, although the Reds will be in action again on Sunday when they host Southampton.
Bournemouth picked up the point which mathematically secured their Premier League status once again with a 2-2 draw against Stoke at the Vitality Stadium.
The Potters, who had not scored in their previous six matches away from home, broke the deadlock on 33 minutes when Bournemouth forward Lys Mousset deflected a corner into his own net.
Junior Stanislas had the Cherries level on 62 minutes when he converted Adam Smith's cross.
Stoke were back in front after 73 minutes through a close-range effort from Mame Biram Diouf but Joshua King's shot deflected in off Ryan Shawcross with nine minutes left.
West Brom ended their goal drought with a 2-2 draw at Burnley, who are not yet completely clear of relegation worries.
Sam Vokes fired the Clarets in front on 56 minutes after a determined run and cross from Ashley Barnes.
The Baggies ended their five-match goalless run when Salomon Rondon equalised in the 65th minute and defender Craig Dawson marked his 27th birthday by heading in a corner with 12 minutes left.
However, the home side secured a share of the points on 85 minutes when Vokes' looping header beat Ben Foster.
Leicester beat Watford 3-0 at the King Power Stadium.
The Foxes, who had earlier hit the woodwork, went ahead seven minutes before half-time when Wilfred Ndidi crashed the ball into the roof of the net after Watford failed to clear a corner.
Riyad Mahrez doubled Leicester's lead just before the hour when the Algerian punished more sloppy defending by the visitors, who are all but safe having already reached 40 points.
Marc Albrighton made it 3-0 in stoppage time following a breakaway by Jamie Vardy down the left.