Sunderland improved after the break but were unable to find a way back into the match, and their day was made even worse in stoppage time when Marcos Alonso was shown a second yellow card.
Below, Sports Mole takes a look at the key talking points from the match.
On target: 7
On target: 2
Was the result fair?
There can be no arguments about the result at Carrow Road. Norwich made a confident start and they never looked back once Snodgrass had opened the scoring. Sunderland briefly threatened to make a game of it in the early stages of the second half, but they had no right to claim anything from their trip to Norfolk.
Manager Chris Hughton will be absolutely delighted with his players. Norwich's key players stepped up and they played as well as they've done all season in the first half. Jonny Howson dominated in the middle of the park, while Joseph Yobo and Sebastian Bassong led the defence impressively. Once again, the strikers failed to find the back of the net despite Wes Hoolahan's best efforts to find his attacking teammates.
It just wasn't good enough from Sunderland. Manager Gus Poyet was clearly furious watching his side struggle to make an impact in the first half and he even felt the need to make two changes before the break. His words at the interval clearly made a difference, but a lack of creativity in the final third meant a comeback was close to impossible. Alonso's red card in stoppage time rounded off a disappointing day at the office.
Sports Mole's man of the match
Wes Hoolahan: The playmaker has had his problems with the club this season, but it's days like today when you realise just how much talent he has at it his disposal. Hoolahan was lively from the first whistle, with his clever passing and direct running causing problems for Sunderland all afternoon.
Alonso has to take this one today. The Spaniard had already upset the Norwich players by going down too easily on more than one occasion. However, it was his decision to handle the ball in stoppage time when on a yellow card which will leave Sunderland supporters scratching their heads.
Phil Dowd was forced to show eight yellow cards, with two going to Alonso, but he had no choice due to the nature of some of the challenges during the game.
Norwich: Hughton's side travel to Wales next Saturday to take on Swansea City.
Sunderland: The Black Cats return to action on Wednesday evening against title-chasers Liverpool at Anfield.