Slaven Bilic saluted his West Ham players for standing up to the pressure after they sank Swansea 1-0.
Cheikhou Kouyate eased their relegation fears, and lifted the heat on manager Bilic, with his first Premier League goal of the season.
Five straight defeats had left West Ham in serious danger of being sucked into the battle at the bottom, and a sixth would have left them just two points ahead of Swansea, and possibly signalled the end for Bilic.
But instead they can breathe easier after moving eight points clear of the drop zone.