The win is their second consecutive over a top-six club after having beat Liverpool last week, and it has now lifted them out of the relegation zone, which seemed impossible only a month ago.
"We are very happy," an ecstatic Carvalhal told Sky Sports after the game.
"We created more chances than them. My players did fantastic work. I told them we are ready to do something different. I said after Watford we are not dead, we are breathing.
"We have a chance (of staying up). We are not in intensive care. We are not far away from the doctor saying we can go home."