The Welsh club, bidding to return to the Premier League for the first time since its relegation in 2018, is now unbeaten in 10 matches in all competitions.
"We are growing day by day, game by game and are nowhere near the finished product," Swansea manager Steve Cooper said. "It was a really good win."
Ghana forward Ayew put the hosts ahead in the 42nd minute at Liberty Stadium, pouncing on a mistake by Canaries goalkeeper Tim Krul, who failed to claim a corner.
Grant Hanley came close to an equaliser before half-time for the away side, but Hourihane netted with a fine strike less than three minutes into the second period.
"It's a massive win," Hourihane said. "We came into this game full of confidence and will keep going full of confidence."
The Ireland international has now scored three league goals in as many matches for the Swans since joining on loan from Aston Villa last month.
"I am loving it here. I am delighted to have the opportunity to play," he added.
"I have high standards and still want more, I am still hungry for more."
Swansea has a game in hand on Norwich, but could slip back out of the automatic promotion spots when third-placed Brentford visits Middlesbrough on Sunday (AEDT).