Davies scored in each half to condemn Norwich to an eighth away defeat of the season and increase the pressure on manager Nigel Worthington.
This was another poor performance from the team tipped for promotion and the Norwich fans showed there frustration by chanting: "We want Worthy out."
Norwich's fortunes will not improve until they rediscover the spark that took them into the Premiership two years ago but on this form any chance of promotion is a long way off.
Derby have also struggled this season but they were quicker and sharper then Norwich all over the pitch and thoroughly deserved to win only their third game at Pride Park this season.
They pushed Norwich back from the first whistle and it was no surprise when Davies fired them in front in the 28th minute.
The on loan Middlesbrough defender drove the loose ball into the net from ten yards after a header from Lewin Nyatanga had stuck Dean Ashton.
The game might have taken a different course if Calum Davenport had shown the same accuracy in first-half stoppage time but the central defender headed tamely wide when he was unmarked at the back post.
The significance of the miss was underlined in the 52nd minute when Davies rose to place a header inside Robert Green's left-hand post when Inigo Idiakez floated in a free-kick.
That was the end of the match and it needed an acrobatic save from Green to keep out another Idiakez free-kick although Norwich substitute Youssef Safri did strike the bar with a 30-yard free-kick.
The only sour note for Derby was the exit of manager Phil Brown who was sent to the stands for kicking over the drinks bottles after he had protested about the award of a free-kick.