Ravel Morrison gave the Hammers a first-half lead but it was cancelled out by Gary Hooper's equaliser from the penalty spot 10 minutes after the break.
Midfielder Robert Snodgrass curled home a sensational free-kick midway through the second period before Leroy Fer struck in injury-time to seal all three points.
After the match, Hughton praised his side for their attitude and strong second-half performance to send them above their opponents and up to 15th place.
"It's a little bit of relief on the back of some really tough games and our performance and the level of our performance hasn't been that bad, but of course we're on the back of two defeats to the two Manchester clubs," Hughton told Sky Sports 1.
"It was good firstly to come back home here and of course to play one of the sides that are not one of the top teams, and I thought we thoroughly deserved it in the end."
As for their poor run of form of late - the Canaries have lost four of their last six games - Hughton hopes this result can turn things around for the club with an away trip to Newcastle and a home clash against Crystal Palace to come before the end of the month.
He added: "Sometimes when you're on a run like we are, there's a little bit of nervousness...what I did see was West Ham score a goal, but I can't think of a real good clear-cut chance that they had in the first period and I think that's the most disappointing thing.
"We were certainly able to raise it in that second half and apart from the goals I thought we had some other very good chances.
"We have to build on this. We had a similar start last season where we had some tough games and didn't start so well, and we had a game here against Arsenal and from then onwards we were a better side.
"It was a bit of a spring forward and let's hope that's today."