The Carrow Road outfit claimed a vital win to ease their own relegation fears and keep Nigel Adkins' side 10 points adrift of safety at the foot of the Premier League table
The first half was largely lacking in quality, although both sides created a smattering of chances despite what was a largely attritional opening period.
Things improved in the second half, as Ryan Bennett and then Elliott Bennett scored two quick-fire goals just after the restart, before Garath McCleary’s shot gave Reading hope.
The Canaries made two changes to the side that lost to Arsenal, with Steven Whittaker and Alexander Tettey making way for Javier Garrido and Elliott Bennett.
Meanwhile, Reading made just one change with Nick Blackman replacing Noel Hunt up front, partnering Pavel Pogrebnyak in attack.
The home side started the strongest and thought they had an early goal when Elliott Bennett shot just wide from outside the penalty area after four minutes.
The Canaries were enjoying almost total domination and nearly took the lead in the 12th minute, as Garrido hit a low shot at the back post that had Alex McCarthy scrambling.
However, the Royals began to exert more influence on proceedings and saw more of the ball as the half went on, taking the sting out of Norwich’s early pressure.
The home fans were growing slightly restless as the Canaries’ initial dominance was replaced by a sustained spell of possession for Reading, although they could not create any clear chances.
The Royals created their best chance in the 42nd minute as a driven Adrian Mariappa cross was turned over the bar by Pogrebnyak with the goal gaping.
Moments later, Norwich created a good chance as Kei Kamara took advantage of a knock-down to hammer a shot that was saved well by McCarthy, with the scores kept goalless at half-time.
The home side began the second half as they began the first, with Kamara forcing a good early save from McCarthy after a superb break forward.
Norwich then took the lead moments later, as a Snodgrass corner caused havoc in the Reading penalty area and substitute Ryan Bennett was there to sweep it home.
Just two minutes later, Norwich had a second as a cross found Holt’s head with McCarthy uncertain in the challenge, and Elliott Bennett was there to put the ball away.
The Canaries were galvanized by their two-goal salvo and were clearly keen for more as they started to dominate possession and the game once again.
Unfortunately for the home side, they conceded in the 72nd minute slightly against the run of play as McCleary let fly with an ambitious shot that Mark Bunn could only parry into his own net.
The Royals were given hope by their goal, as they went searching for the crucial equaliser in the closing stages of the game in their fight against relegation from the league.
However, despite the away side’s best efforts, they were unable to score another as Norwich clung on for what might be a crucial win.