Hughton had faced criticism from supporters following a 4-2 defeat to Southampton last time out, but saw his players deliver a fine response at Carrow Road on Saturday.
First-half goals from Robert Snodgrass and Alex Tettey, who found the net with a sensational volley from 30 yards, secured a valuable win to lift Norwich seven points clear of the bottom three.
Hughton - now Norwich's longest-serving manager in the Premier League - underlined the importance of beating a rival in the battle to avoid relegation, with Sunderland sitting 18th.
He said: "We wanted a reaction from last week. We didn't shy away from the fact we knew this was a big game because of who the opposition were.
"I thought we were excellent from start to finish. I think that was one of our best performances of the season. We have had good ones before. I remember (against) Manchester United here for 45 minutes we were very good.
"We have had better performances but you have to score the goals at the right time and in that first-half period when we were good we got those goals."
Hughton reserved particular praise for Tettey following the Norwegian's spectacular strike.
"I think everybody would have enjoyed that second goal and it could not have happened to a nicer fella," Hughton added.
"He is a good individual and professional and that was probably why there was that type of response. Alex is not going to score too many like that in his career.
"When you are a player and you score that type of goal and you know it is going to be shown over and over it is a really nice feeling and the lads are delighted for him."
Sunderland manager Gus Poyet, meanwhile, claimed he is not worried about relegation despite the defeat at Carrow Road.
He said: "When we only had one point earlier in the season when everyone else had seven or eight, I was worried. But now we are back in the mix with games in hand.
"Of course, I try to do my best but I'm not that worried. The situation is that if we keep looking at the rest and thinking other results were good for us today, then we are going to forget that we need to play ourselves, for 90 minutes every game.
"It doesn't matter who you play against or where you play, you need to make sure you do your bit because that's what you get paid for."