Cardiff almost took the lead in the first minute. Craig Noone delivered the ball from the right and Jordon Mutch tried an audacious overhead kick, but he did not get enough power on the strike to beat the goalkeeper.
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Norwich came back and Jonas Gutierrez headed over, but the visitors grabbed the opening goal with just five minutes played.
Norwich continued their strong start with some good football, but Cardiff's Steven Caulker missed a good chance to equalise for the home side when he headed wide.
The Bluebirds were sloppy in possession, but Noone did drill a low shot just wide of the post.