Ryan Bennett nodded home a Robert Snodgrass corner with three minutes of normal time remaining at Carrow Road to move Norwich five points clear of the bottom three.
The win was Norwich's first in 10 games in all competitions, but they made it hard for themselves with a desperate wastefulness in front of goal.
Just three of their 23 attempts at Allan McGregor's goal were on target, and they have only managed 11 goals from as many Premier League games on home soil this term.
But the ex-Newcastle United boss was delighted to seal a precious win, and hopes it can boost his squad's morale ahead of a midweek clash against his former club.
"We are talking about small margins and big wins," Hughton said. "These three points become even bigger.
"You are then looking at the results of other sides, which is something you shouldn't do, really. The tighter it gets, the wins get bigger.
"These are big wins. We will enjoy it today as we have a big game coming up."
