West Ham have been dragged back into the thick of the relegation battle after back-to-back 4-1 defeats to Liverpool and the Swans. This time Andre Ayew's header was saved by Adrian, but it fell nicely for King to stab the ball home.
The victory also marked the return of midfielder Leon Britton, who had spent the past four months on the team's coaching staff while dealing with injuries before being asked by Carvalhal to focus once more on playing.
Carvalhal, who guided the Swansea to their first FA Cup quarter-finals since 1964 this week, believes results at home remain crucial to their top-flight survival bid.
Chris Wood came off the bench to inspire Burnley's second-half fightback which earned a 2-1 English Premier League win against Everton.
On average, the number of points to guarantee survival in the previous 22 top flight seasons is 36.6.
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"Marko Arnautovic had a decent game at Liverpool".
The Ayew brothers have been backed to cause double trouble and free Swansea from their Premier League relegation worries. With only one goal separating the teams at the interval, West Ham could not live with the extra intensity Liverpool brought to the second half.
Carvalhal preferred not to single any one player out for credit, saying: "When we win 4-1 it's not about one player".
Swansea have scored 14 goals in nine league matches under Carvalhal, having scored just 11 in their previous 20 this season before his appointment. We are better and better, we are really strong at the moment.
You always want to keep your best players but there's no truth in that yet.
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"We have trained hard at corners this week, movement, and we scored twice from them".
The win meant Spurs' Argentine manager Mauricio Pochettino became the first non- European coach to win 100 Premier League games.
'What we can't do now is have another bad day at Huddersfield next week, we need to stay sharp and stay focused'. He's an important player for us so we hope it's not too bad.
We didn't look up for it at Brighton like we did against West Ham, there was a massive difference and it was good to see that sort of turnaround in attitude.
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