Michael Turner headed against the bar for Norwich after the break before Hooper was denied by Michel Vorm.
Dyer injury overshadows point - Laudrup
Swansea's Dutch goalkeeper needs to have an operation on a niggling knee injury but no decision has yet been made as to when he will go under the knife.
And the Welsh side were glad of his return between the posts as his fingertips kept Hooper's close-range effort out to avoid defeat for a Swansea side, playing their third game in six days.
A shin injury prevented Hooper, 25, from making his Premier League Canaries debut until late September after joining from Celtic for £5m and, after failing to score in his first five league games, he has started to repay manager Chris Hughton's faith in him with four goals in little more than a month.
Swansea, who are yet to beat Norwich in five Premier League meetings, will be concerned with just two wins from nine but still sit tenth in the table, two points and four places ahead of Norwich.
Norwich's summer signings
Left-back, undisclosed fee from Lazio
Winger, £3.2m from Birmingham
Ricky van Wolfswinkel:
Striker, £8.5m from Sporting Lisbon
Left-back, undisclosed fee from Blackburn
Goalkeeper, free transfer from Stoke
Midfielder, undisclosed fee from Twente
Striker, undisclosed fee from Celtic
Michael Laudrup's men, who qualified for the knockout stages of the Europa League in midweek, top both the possession and pass accuracy charts in the Premier League this season and you could see why as they started the game well with their brand of patient, passing football.
But their opener was very un-Swansea like as the alert Dyer capitalised on a defensive mix-up after Ashley Williams' hopeful long clearance caught out Bassong.
The Cameroon international misjudged the flight of the ball and, lurking on the defender's shoulder, Dyer flicked the ball on with his head before smartly lobbing the onrushing Ruddy.
Swansea monopolised possession for long periods but weak defending from Williams nearly gifted Norwich a leveller.
Gary Hooper shrugged off the defender just outside Swansea's box, took the ball to the side of the advancing Michel Vorm, but with two defenders on the line he could only blaze wide and over.
Swansea, who have just welcomed Wilfried Bony and Michu back from injuries, then had Dyer stretchered off after receiving oxygen from paramedics. The midfielder looked to land awkwardly on his ankle after being beaten in the air by Bassong.
Then, just before half-time, Leroy Fer had a shot headed off the line by Williams before Hooper brilliantly volleyed the Canaries level.
Hooper goal 'very special' - Hughton
The former Celtic man collected Johan Elmander's chest down before looping a volley spectacularly over Vorm and into the net.
After the break Norwich were inches from taking the lead when Michael Turner's looping header hit the bar before hitting Swansea defender Jordi Amat on the back of the head and clearing the bar.
After Hooper was denied by Vorm, Swansea went close to the winner themselves when Jonjo Shelvey burst through onto goal before having a low shot smothered by Ruddy.
Norwich manager Chris Hughton:
"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. It was important we didn't lose the game.
"It was a very special goal. They are the ones you don't bank on. What you expect from your strikers is them to score run of the mill goals. The bonus ones are when something out of nothing is produced.
"He showed great technique."
Swansea manager Michael Laudrup on Nathan Dyer's injury:
"The health of a person is the most important thing. We know football can have injuries. Hopefully I'm wrong, but this looked much more serious.
"We have to wait a couple of days for an X-ray and a scan, and we all cross our fingers to hope it is not that bad. That will overshadow everything else. It is just a game of football.
"That game of football we controlled quite well in the first half and then just before half-time, after the injury, we had 10 minutes where we lost a little bit of perspective and they scored a fantastic equaliser."
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