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The Rams started the game on the front foot, and within the first few minutes of the game 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.
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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.
The Rams picked up from where they left off after the interval, but were wasteful in the final third and from set pieces, nearly paying the price when Austin almost converted Armand Traore's cross in the 55th minute.
On the hour, Gary O'Neil was sent off for QPR after hacking down Russell just outside the area, but Ward wasn't able to make the most of the subsequent free kick.
Derby continued to turn the screw against their 10-man opponents, Craig Bryson forcing a good save out of Green with a low drive before teeing up Chris Martin, whose effort rattled the outside of the woodwork.
Just when it seemed like the game would go on to extra time, a defensive error by Richard Keogh gifted the ball to Zamora, and the substitute steered the ball beyond Lee Grant's dive to send the blue and white half of Wembley into raptures.