Dusan Tadic scored twice as relegation-threatened Southampton boosted their chances of Premier League survival with a 2-1 victory over south coast rivals Bournemouth.
Struggling Saints had not won in the top flight at St Mary's since November but the recalled Tadic changed that with a goal in either half to end a nine-game winless league run.
Bournemouth had briefly threatened to damage their near neighbours' safety hopes when Josh King levelled in first-half added time.
The game also marked a first Premier League victory under Mark Hughes -- and took them to within a point of Swansea after they lost 1-0 at home to Chelsea.
Chelsea's chase for a top-four spot gathered pace as Cesc Fabregas scored his 50th Premier League goal.
Swansea had their opportunities, particularly in the second half, to claim something, but the defeat means it is now six games without a win for Carlos Carvalhal's side.
There is also little breathing space for Swansea now in the fight for top-flight safety, with other sides at the bottom of the table also picking up vital victories.
Crystal Palace all but confirmed their place in the Premier League for next season with a 5-0 win against Leicester that took them six points clear of the relegation zone.
Wilfried Zaha was Palace's key man as usual, scoring his fourth goal in four games to put them ahead on 17 minutes after an impressive passing move that included a backheeled assist from James McArthur.
Zaha returned the favour shortly afterwards, showing excellent vision to pass to McArthur in the penalty area, the midfielder swivelling and firing low past Ben Hamer in the Leicester goal.
Leicester's day got worse as Marc Albrighton was sent off for a foul Zaha, and, down to 10 men, Leicester conceded further goals to Ruben Loftus-Cheek, Patrick Van Aanholt and Christian Benteke.
Cenk Tosun and Idrissa Gueye scored in either half as Everton piled the pressure back on relegation battlers Huddersfield with a 2-0 win at the John Smith's Stadium.
Turkey forward Tosun's clinical finish gave Everton a half-time lead and Senegal midfielder Gueye blasted home their second with 13 minutes left.
It was a damaging defeat for Huddersfield, whose victory over Watford in their last match had given their survival hopes a big lift.
A seventh home loss of the season, though, coupled with wins for relegation rivals Crystal Palace, Southampton and West Brom, has left David Wagner's side three points above the drop zone.
Premier League leading scorer Mohamed Salah had a rare off day as Liverpool continue to stumble towards guaranteeing a top-four finish after a goalless draw at home to Stoke.
However, it was even more damaging for struggling Stoke, whose point failed to see them escape the bottom three. With all their relegation rivals having games in hand, their top-flight future looks bleak.
Jurgen Klopp's side still require a maximum of four points from their last two matches -- including next week's crucial trip to Chelsea -- but equally worrying were injury scares for Jordan Henderson and Salah ahead of Wednesday's Champions League semifinal second leg which they lead 5-2.
Matt Phillips gave West Brom a glimmer of hope in their fight for Premier League survival as they won 1-0 at Newcastle to extend their unbeaten run to four games.
Phillips' 29th-minute strike handed caretaker boss Darren Moore a second victory of his brief reign as the Magpies came up short in their hunt for a fifth straight home win in front of a disappointed crowd of 52,283 at St James' Park.
It was no more than the visitors deserved as they created the better chances on an afternoon when they knew even three points might not be enough to keep them in the top flight.
In Saturday's other game, Burnley are virtually assured of European football next season for the first time in over 50 years after picking up a point in a 0-0 draw with Brighton.
Everton's victory at Huddersfield means the Clarets are not mathematically assured of a top-seven finish, and a place in next season's Europa League, though they are six points clear of the Toffees with two games remaining, and have a far better goal difference.
Burnley, whose last European campaign was during the 1966-67 season, came closest to scoring at Turf Moor when Kevin Long hit a post in the first half, yet Brighton also picked up a valuable point in their battle to avoid the drop.