The first Premier League side to be relegated was confirmed on Saturday, while West Bromwich Albion kept their slim survival hopes alive by beating Tottenham Hotspur.
Stoke City 1-2 Crystal Palace
Stoke City were relegated to the Championship after 10 years in the Premier League after losing 2-1 to Crystal Palace.
The Potters took the lead through Xherdan Shaqiri's fine free-kick in the 43rd minute, before Palace hit back through James McArthur and Patrick van Aanholt.
Bournemouth 1-0 Swansea City
Bournemouth sealed a spot for another season in the top flight following their 1-0 win over Swansea City, with Ryan Fraser getting the all-important goal in the first half.
Leicester City 0-2 West Ham United
West Ham United edged closer to confirming their survival with a 2-0 win over Leicester City.
Joao Mario and Mark Noble netted in the first and second stanza respectively as the Foxes fell flat at the King Power Stadium.
Watford 2-1 Newcastle United
Watford ended a poor run of form to beat Newcastle United 2-1.
Roberto Pereyra and Andre Gray got the two goals for Watford in the first half and Ayoze Perez pulled one back for United but they could not avoid defeat.
It could have been a comfortable win for Watford but Troy Deeney missed a penalty in the first half.
West Bromwich Albion 1-0 Tottenham Hotspur
Relegation-haunted West Bromwich Albion postponed their fate for another week after shocking Tottenham Hotspur with a 1-0 win in Saturday's early game.
Jake Livermore struck in second-half stoppage time to seal a victory that extended their Premier League fate to another week, although it is now out of their hands.
Everton 1-1 Southampton
Everton struck in the dying moments of the second half to earn themselves a 1-1 draw with Southampton on Saturday evening.
Nathan Redmond broke the deadlock for the Saints four minutes before the hour but they were dealt a blow as Maya Yoshida was sent off five minutes before time.
The Toffees struck deep in stoppage time thanks to a deflected effort from Tom Davies.