West Ham secured their first league win in eight games to ease the pressure on under-fire boss Slaven Bilic.
Heading into the clash, reports suggested the Croatian would lose his job should the Hammers suffer defeat against the Swans.
But the Hammers board were not forced into action as Cheikhou Kouyate’s late first half strike delivered three points for the hosts.
The result leaves West Ham eight points clear of the relegation zone, while the Swans remain two points from safety.
Liverpool secured a crucial win in their quest to qualify for the Champions League after coming from behind to beat struggling Stoke.
The Potters went ahead through Jonathan Walters in the first half to leave Jurgen Klopp’s side in serious danger of slipping out of the top four.
But the Brazilian duo of Philippe Coutinho and Roberto Firmino ensured the Reds claimed all three points, as they stepped off the bench to make a telling impact.
The result leaves Liverpool nine points clear of Arsenal and Manchester United – but have played three games more.
Middlesbrough slipped further towards the Championship after failing to beat Burnley at the Riverside Stadium.
The hosts had plenty of chances to force an opening, but it was not to be as the Clarets somehow escaped with a point.
The result leaves Boro six points adrift in 19th place.
Manchester City boosted their hopes of qualifying for the Champions League after easing past Hull at the Etihad Stadium.
Pep Guardiola’s side were made to wait until the half-hour before finding a breakthrough goal as Ahmed El Mohamady put the ball into his net.
And further goals followed as second half strikes from Sergio Aguero and Fabian Delph gave the hosts a comfortable lead before Andrea Ranocchia’s late consolation goal for the Tigers.
Southampton edged closer to securing an eighth place finish for a third consecutive season after beating West Brom at The Hawthorns.
The Saints claimed all three points thanks to a fine strike by Jordy Clasie as Claude Puel’s side moved within four points of the Baggies.
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