Wayne Rooney's side had to fight hard for the points, ending a nine-game run without a win in the league.
It was 32-year-old debutant, Sam Baldock, who scored the only goal of the game for Derby.
His predatory shot in the 57th minute was enough to seal the result, which lifts the pressure on Rooney for the time being.
Derby now move into a mid-table spot with four points from their first three matches.
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