Cheikhou Kouyate admitted his matchwinner against Swansea was his most important goal for West Ham.
The Senegal midfielder lashed a powerful drive past goalkeeper Lukasz Fabianski moments before half-time to secure a vital 1-0 win.
The Hammers had lost their previous five matches and were in danger of being dragged into the relegation battle.
But Kouyate's strike lifted them eight points clear of the drop zone and eased some of the pressure on manager Slaven Bilic.
"This victory is very important for the team because we have had a few difficult weeks and now this victory is good for the fans, for the players and for the staff," Kouyate told the club website.
"This is my most important goal for West Ham and it came in a good moment, but the really important thing was not the goal, but the three points.
"There was big, big pressure because the team needed to win this game. Now we can go to Sunderland next week and fight for some points and go for the win."
The only downside for West Ham was a hamstring injury suffered by top scorer Michail Antonio, although Bilic expects the winger to be back before the end of the season.
"Unfortunately for us, Michail's injury came out the blue," Bilic said.
"We have to stay positive. Michail is like superman - he's always ahead of schedule. I expect he'll be back very soon."
For Swansea, a fifth consecutive away defeat leaves them in 18th, although they will at least be heartened by Hull losing at Manchester City to keep them in what increasingly appears to be two-horse race to avoid the last relegation spot.
"We still have six games to go and we must go into each one looking to win," midfielder Leroy Fer told the club website.
"Watford is next up on Saturday. It's going to be a hard game again, but we have to stay positive and go there to win.
"It's going to be massive, but every game left is like a final now."