West Ham captain Mark Noble has called the win over Swansea their "biggest in a few years", as his team moved eight points clear of the relegation places.
Cheikhou Kouyate scored the only goal at London Stadium, as the Hammers ended a run of five straight defeats.
West Ham are 14th with six games left and midfielder Noble says one more win should secure their top-flight status.
"We haven't been good enough for a couple of months, but this should release the pressure," he said.
Before Saturday's game, Slaven Bilic's side had gone seven matches without a victory and won only one in nine to be dragged into the relegation battle.