Norwich had not won at home since November and, despite being the better side for much of the game, needed a late headed winner from Ryan Bennett to pick up their first victory in eight games and put a little breathing space between themselves and the Barclays Premier League relegation zone.
Hull, who could have gone ahead when debutant Nikica Jelavic hit a post inside the opening two minutes, ended the game with 10 men, with Tom Huddlestone seeing red for a second yellow card late on, but could have no complaints that they left Carrow Road without a point.
Hughton's future has been under intense scrutiny all week following a 3-0 thrashing at Fulham in their FA Cup third-round replay, with the club's chief executive David McNally saying his job was safe as long as he kept Norwich out of the bottom three.
This win opened up a five-point gap to the relegation zone and Hughton was delighted with the response from his beleaguered players.
"We knew this was a big game," he said.
"I want to do the best job that I can, because with every manager there is a trust put in them to develop a group of players and do as well as you can.
"I saw it as a big win. It is so tight down there it is very difficult to talk about must-win games, but I know it is an important win - for the fact the opposition are close to us in the division and it is a close game.
"You have to not panic and be composed, things can change over one game or a two-game period.
"It is never nice when there is a lot of criticism around, but it is part and parcel of the game and for any criticism that I might have had or feelings about my job, maybe next week it will be someone else.
"The good part about this game is there is always the challenge of the next one."
Ricky van Wolfswinkel, who has not scored since the opening day of the season, and Robert Snodgrass had the best of Norwich's chances throughout the game, but it was Bennett, scoring his first goal since April, who settled the match.
Hughton admitted he started to think it would not be his side's day in front of goal.
When asked if he was worried they would not find a winner, he said: "I was concerned, yes.
"On the balance of the game I don't think there is anybody that could not agree that we deserved to win the game. I thought we were the better team over 90 minutes, but they are a good side and defend very well.
"We perhaps didn't create enough clear-cut chances, but we put them under a lot of pressure. At that stage of the game there is a part of you that thinks, 'It isn't going to be our day', but the lads were resilient."
Hull boss Steve Bruce was left ruing the early miss from new-boy Jelavic, but felt his side did not do enough to leave with three points.
He said: "We had a big chance in the first couple of minutes when Jelavic hit the post and Liam Rosenior had a really big chance, but overall in the second half we were a touch disappointed with how we handled the ball.
"He [Jelavic] has done everything right. His connection with it was right, he struck it really well and I was expecting it to nestle in the back of the net. It has hit the post and missed by two inches. What a start that would have been for the lad.
"When you play like that away form home, to come away with a point would have been terrific for us, another point on the board, but it wasn't to be."
Bruce has been praised for his side's start to life in the top flight, but the win for Norwich takes them level with the Tigers.
The former Canaries defender believes he has been exempt from the pressure placed on Hughton because less is expected of his players.
"It is about expectation," Bruce said.
"We are a newly-promoted club. Everybody expects us to be in the bottom three and when you have been here for two or three years everybody expects you to be in the top six. That is how it is in the Premier League, but Chris has been around it a long time."