The Rams spent most of the first half on the front foot, playing confidently and getting most of the chances against Harry Redknapp's outfit.
Within the first few minutes, Johnny Russell skipped past several QPR challenges and fed the ball to Will Hughes from the edge of the area. The youngster was hacked down to gift the Rams a free kick, but Russell blasted the ball into the wall.
Charlie Austin then launched a speculative effort into the stands for QPR in the eighth minute, but the Rams had arguably the best chance of the half in the 24th minute when Craig Forsyth sneaked into the box unmarked and sent his header just over the bar.
Towards the end of the first period, Robert Green had to be at his best to deny Jamie Ward's in-swinging free kick which looked to be creeping into the bottom corner, but the ex-England goalkeeper was able to get down low to keep the effort out.