Two goals in the first ten minutes put Villa in control.
The Canaries started brightly, but went behind in the seventh minute when they gave a corner away and poor marking from the set-piece allowed Villa to score from a Magnus Troest header.
City's misery deepened just three minutes later when a mistake by the defence allowed Villa to double their lead through Gabriel Agbonlahor.
Norwich were unable to get into their stride for the remainder of the half and despite having the wind in their favour when the match restarted after the interval, they could not make this advantage count.
The Canaries still felt they could get back into the game, but their hopes were ended when Villa scored their third in the 65th minute, again through Agbonlahor.
Shane Herbert - couldn't prevent
defeat in the City goal on Saturday