The Canaries trailed to a Ravel Morrison goal at half-time but took all three points after a Gary Hooper penalty was followed up with a Robert Snodgrass free-kick and a stoppage time strike from Leroy Fer.
The win takes Norwich to 15th in the table, leapfrogging West Ham in the process, and Hughton is pleased to get back to winning ways following a difficult spell which culminated in a 7-0 thrashing at the hands of Machester City last weekend.
"It will be a massive lift for the players," he said.
"There is no doubt psychologically that it is a blow to be in the bottom three.
"Hopefully it will give us the lift we need and I'm pleased for everyone at the club. It is a very good result for us at this particular time."
Hughton has been one of the favourites to lose his job in recent weeks but said after the victory that he does not pay attention to speculation and is used to dealing with stress.
"I have been around a long time now," he added.
"Of course I am aware of things that are said but that comes with the territory.
"You can't expect to have things easy when it is not going well, that goes with the territory - but this is a fantastic club with fantastic owners.
"I always speak about the team and how pleased I am for them but I'm equally as pleased for the people upstairs.
"It is part of the job, is it stressful? Yes it is. It is stressful next week and the week after but you have to work as hard as you can and do things as well as you can. You have to have belief in your own abilities."
West Ham boss Sam Allardyce, who labelled the game a six-pointer during the week, was left bemoaning a mistake by experienced goalkeeper Jussi Jaaskelainen.
The Finn failed to hold a straightforward Michael Turner header and clipped Hooper as he looked to rectify his error, leaving Allardyce to regret a moment which proved to be a turning point.
"There's never been as big a change around in fortunes for a long time," he said.
"Jussi made three mistakes in one. He loses the first one, tries to grasp it again and gets so desperate he went lunging to try to get himself out of trouble and ends up giving the penalty away.
"At that stage you wouldn't expect us to do anything other than go on to win, that makes it more difficult to take. It really stunned me and how it came about - but it has.
"I expected us when we got that goal to win it and we can't blame anybody but ourselves because we've gifted Norwich the opportunity to lift themselves, lift the crowd and win it."
- Sports & Recreation
- Gary Hooper
- Robert Snodgrass
- Ravel Morrison