The Czech striker pounced in the 70th minute after Rangers goalkeeper Alex Smithies failed to hold a Tom Ince shot to give the Rams the points in a game they dominated.
QPR were poor, although they almost snatched what would have been an undeserved point when Idrissa Sylla hit a post two minutes from the end.
Rowett had stuck with the team that started at Nottingham Forest before the international break but Ian Holloway made four changes from the side that won so convincingly against Rotherham last time out.
Derby were first to threaten, with David Nugent just straying offside in the 12th minute before Johnny Russell was played in on the left by Ince two minutes later but dragged a shot wide of the far post.
There was more encouragement for Derby in the 20th minute when Smithies misjudged a cross and Russell failed to connect as he slid in at the back post and the Rangers goal came under threat again seven minutes later.
A Vydra free-kick was deflected to Russell who shot straight at Smithies and a minute later the keeper had to beat out a Nugent shot when his defence was exposed on the break.
Derby were dominating possession and had another chance in the 37th minute when Russell glanced a header wide under pressure from Nedum Onuoha.
Nugent fired wide on the turn in the 43rd minute and Rangers were relieved to hear the whistle at the end of a half in which they had been well off the pace.
There were no early signs of improvement in the second as Nugent failed to connect with a cross from the left before a careless pass allowed Russell to break away in the 53rd minute but he hesitated and his shot was blocked.
It was no surprise when Holloway made a change, but Derby were still dictating and deservedly went ahead in the 70th minute when Russell came in from the left and set up Ince whose shot was spilled by Smithies for Vydra to fire into the roof of the net from eight yards.
Rangers had not posed a threat in a desperately disappointing performance but had two chances in less than a minute as Derby suddenly looked nervous.
First Matt Smith turned inside the box in the 88th minute to hit a low shot which Scott Carson turned behind and from the corner, Idrissa Sylla headed against a post but it was too little, too late.