Norwich kicked off and took the lead in the ninth minute when Clint Easton collected Paul McVeigh's through ball and beat Mike Pollitt with a crisp right foot strike from 12 yards.
After Damien Francis had fallen victim to some shirt-pulling, Martin McIntosh was booked in what appeared to be a case of mistaken identity.
In the 28th minute, Norwich had the ball in the net but Francis had his effort ruled out for offside.
However, when McVeigh crossed from the left on the half-hour, Mark Rivers made no mistake with a well-placed header across goal, which found the net inside the near post.
It could have been 3-0 five minutes later, but Pollitt did well to keep out a stinging drive from City captain Adam Drury.
Chris Sedgwick was booked for a foul after 36 minutes and two minutes later Pollitt was smartly down to save a low shot from Rivers.
In the 53rd minute, the Millers had their first corner but Robert Green saved the resulting header from Chris Swailes.
A minute later, McIntosh was lucky to escape a red card when he fouled David Nielsen just outside the penalty area as he was about to shoot.
Nielsen then headed over when Easton picked him out with a left-wing cross.
On 66 minutes, McIntosh was shown the red card for chopping down McVeigh and Richie Barker made way for Gary Branston three minutes later.
Norwich introduced loan-signing Elvis Hammond with 11 minutes left. McVeigh was the player withdrawn. Nielsen followed four minutes from time to be replaced by Zema Abbey.
The only disappointing feature for Canary fans was the lack of further goals.