A second-minute header from Adam Bolder was good enough to clinch the points, although Plymouth had enough chances to have got something from a game spoiled by a strong icy wind.
The visitors also had Paul Connolly sent off after he collected two yellow cards but, they can take some consolation from the way they bounced back from conceding the early goal.
David Norris wasted three good shooting opportunities and Plymouth's finishing was not up to the standard of their approach play.
Derby looked nervous despite the boost of the early goal and had to endure a number of anxious moments before the final whistle sparked celebrations at Pride Park.
There was also another show of strong protest against the current board, but at least on the field Derby are starting to move towards Championship safety.
They now have a nine-point cushion between themselves and the relegation zone and it is unlikely they will be dragged into the battle for survival with games starting to run out.
This was hardly a vintage performance as Plymouth pushed the home side back after Derby looked comfortable for the first quarter of the match.
Bolder gave them the perfect start when he headed Tommy Smith's cross just under the bar, but Plymouth almost hit back with Norris firing over from 12 yards after Vincent Pericard had set him up.
Pericard provided another opening for Norris in the 50th minute but he shot straight at the keeper and Nick Chadwick also sliced well wide when he should have done better.
Norris again drilled a drive straight into the grateful arms of Lee Camp on 69 minutes and then provided sub Akos Buzsaky with a chance that the Hungarian put into the side-netting from a tight angle.
Connolly was dismissed for his second foul on Smith but it was Plymouth's 10 men who looked more likely to score, although Kevin Lisbie's control let him down when he was away in the 86th minute.
It proved one of those days for Plymouth, who could not hit the net and their last chance went when Buzsaky struck a volley straight at Camp two minutes from time.