Wolves lived up to their billing as one of the promotion favourites while Derby looked well short of genuine candidates to bounce back to the Premiership at the first attempt.
Dave Jones' side overpowered Derby in the closing stages and it is clear that Wolves have shaken off the disappointment of missing out in last season's play-offs.
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It might have been different if Malcolm Christie had not headed wide from an unmarked position ten yards out in the 76th minute.
Within two minutes, Cooper had scored against his former club with a shot that took a wicked deflection and Wolves never looked back.
Rae volleyed in the third in the 88th minute and in injury time, Miller tapped in from close range after Nathan Blake had opened Derby up on the left.
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The match was evenly poised until Cooper's moment of good fortune but Jones believes his team are more formidable this season.
"Believe me, we are stronger than last year and that's primarily because of the players I have brought in.
"Once we went a gear up I thought some of our football was awesome at times."
For Derby manager John Gregory, the picture is bleaker. He was without several key players through injury and goalkeeper Mart Poom and striker Fabrizio
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Gregory said: "They got a rather fortuitous second goal and I thought that at 1-1 I could only see Derby winning it.
"But it's now over 12 months since we've won two consecutive games and that's an appalling statistic for any team."