Some late pressure from the Canaries saw them try and find a way back into the game but their lack of creativity meant they were unable to break down the Swansea backline.
Story of the match
The game started off fairly cagey as both sides tried to work each other out. It was a slow burner but halfway through the first half, the game started coming to life.
The two high flyers looked to do the right things with Norwich keeping the ball with great intent, looking to break down a Swansea's defence that is the best in the league.
Swansea also began in their usual style, their back three turned into a back five when they were defending and they restricted Norwich to any clear cut chances, whilst also creating a few opportunities themselves.
The first notable chance of the game came 23 minutes in when Canaries talisman, Teemu Pukki, found space but he just couldn't direct his effort goalwards.
Swansea began to settle into the game the longer the half went on, forcing Norwich to commit nervous fouls in their own half.
In the 42nd minute, their defensive resilience and attacking pressure paid off when Norwich goalkeeper, Tim Krul failed to collect the ball from a corner and after a scramble in the box, the ball fell to Ayew who made no mistake in passing the ball into the net.
The Swans managed to go into the half-time break leading despite a 45th minute Grant Hanley header which forced an alert, Freddie Woodman, into action.
It didn't take long for the Swans to impose themselves on the second half either, when just 3 minutes into the second period, Hourihane doubled their advantage and scored his third goal in as many games.
A loose Kenny McLean pass was picked up by Jay Fulton who's sideways ball found Hourihane and from 25 yards out, he battered a low-driven, perfectly accurate strike into the bottom right corner, giving Krul no chance.
The story of Norwich's night was adequate approach play followed by inadequate finishing. The Canaries managed just three shots on target all game and failed to score for the third league game in a row.
The build-up play from Daniel Farke's men was hard to fault but the Swansea backline proved why they have the best defensive record in the league by making it hard for Norwich to get any clear sights of goal.
A triple substitution in the 57th minute set out Farke's intentions as he introduced Adam Idah, Mario Vrancic and Onel Hernandez.
Norwich looked to attack in more numbers and as a result, they were countered on a few occasions and Swansea could have been awarded a penalty in the 81st minute when Ben Gibson tangled with Jordan Morris.
Despite some late pressure from the Canaries, they were unable to find a way through and are now without a win in three Championship games.
Stand out player
Conor Hourihane - Swansea City
The loan signing of Horuihane for Swansea has proved to be very impressive.
He put in another admirable performance this evening, controlling the tempo of the game, dictating the midfield and putting in a disciplined defensive display.
His goal was excellently taken and gave the Swans an important bit of breathing space just after half-time.
Takeaways from the match
Swansea can defend
Cooper's men boast the best defensive record in the Championship and have now kept 14 clean sheets and conceded just 15 goals all season.
They were extremely resolute again tonight and Norwich struggled to break them down.
The combination of Kyle Naughton, Ryan Bennett and Marc Guehi worked perfectly this evening.
Another tough night for Norwich
Norwich have failed to win for three Championship games and are without a goal in all three of them.
Whilst the previous two were goalless draws, they have struggled to find the net, even with their main man, Pukki, in the starting lineup.
They look to be really missing the lively Emi Buendia and whilst Norwich are not a one-man team, he is a figure which they will be excited to welcome back once he returns from suspension.