A first-half goal from Robert Snodgrass and a fantastic strike by Alexander Tettey sealed a vital 2-0 win for Hughton's side as they outplayed Gus Poyet's side, with the Black Cats struggling to have an impact on the game.
Marcos Alonso was sent off late on for the visitors, who remain inside the bottom three while Norwich move seven points clear of the relegation zone.
With Hughton's position at Carrow Road seemingly questioned on a weekly basis, defeats for fellow strugglers Crystal Palace, Fulham, Cardiff and West Brom made for good reading for the 55-year-old.
"It has been a good day for us," he said.
"More important than those results it has been a good day for us here. Ultimately, the results from now until the end of the season will determined where we are and we have to make sure our results our good enough.
"It is important to have a big a gap from where we are to the bottom three as possible. Last weekend we lost and other results didn't go our way, today they did."
Hughton made five changes to the side that lost 4-2 at Southampton last weekend and he was pleased with the response as his players raced into the lead and closed the game out when necessary.
"I thought we were excellent," he added.
"We wanted a reaction and we didn't shy away from the fact we knew it was a big game. We knew it was big and I thought we excellent from start to finish.
"They changed things and got the extra player up front. We have been good here at Carrow Road this year and haven't conceded many goals, that is equally as important."
Poyet was also aware that results elsewhere had cushioned the blow of defeat but will not be relying on other sides to help him in his quest to keep Sunderland in the top flight.
"I try to do my best but I'm not worried," he said.
"If we keep looking at the rest and that results went good for us today, we forget about ourselves. You need to make sure you do your bit because that is what you are getting paid for."
Poyet made two tactical substitutions five minutes before half-time but refused to single out Ki Sung-yueng and Jack Colback, the players hauled off, and was left upset by a slow start.
"They made me make decisions I don't like - I don't like changing players in the first half. It wasn't a case of one or two players, It was seven or eight but you cant change seven or eight," he said.
"I think it is very disappointing when you start a game with the importance of today the way we did.
"We started badly and we weren't getting close to any of the action. I think it was a mix of being bad on the day and Norwich being very brave."