Hughton's men extended their unbeaten home run in the Premier League to four matches, despite falling behind to Nathan Dyer's lofted effort.
Dyer was subsequently carried off on a stretcher with a suspected fractured ankle, and the momentum appeared to shift in Norwich's favour after the incident.
The Carrow Road outfit equalised deep into first-half injury time thanks to Gary Hooper's stunning volley, who had earlier put a good opportunity wide when one-on-one with Michel Vorm.
Norwich then missed several chances after the interval, with Hooper again coming close and Michael Turner seeing a header rebound off the crossbar.
Hughton said: "Swansea have had a tough week. I thought we very much edged it in the second half.
"We conceded a poor goal, showed great character, and needed a special goal to get back into it.
"I thought if anyone was going to score in the second half it would be us. (But it was) Important we didn't lose the game."
Hooper was delighted with his strike, which brought the home supporters to life, but also rued Norwich's inability to finish their other chances.
"It was a great ball (by Steven Whittaker) for my goal, a great chest down (from Johan Elmander) and I just looped it in," Hooper added.
"I had to make up for the one (when) I went round (Vorm) and missed. It sat up nice for me.
"We had a few chances; they (Swansea) have had a long week. I thought we played well in the second half but didn't take the chances."
