Two goals just before the interval and another late on ensured the Reds remain without a win in their last six outings.
The game got off to a slow start but it was the hosts’ Mamadou Thiam who unleashed the first effort on target only to drill a shot straight down the throat of Scott Carson.
A minute later Harvey Barnes cut inside and smacked a sweet shot which Carson managed to tip behind for a corner.
Barnsley had arguably been the better side but it was the visitors who were to open the scoring against the run of play on 39 minutes.
Andreas Weimann clipped the ball into the box and Tom Lawrence was on hand to cut inside and fire past Adam Davies. The Reds’ stopper got a hand to the shot but it wasn’t enough to prevent it from going in.
And it went from bad to worse just five minutes later when the hosts were caught napping again.
Chris Baird fed the overlapping Weimann and his pullback found Vydra who slotted past Davies with consummate ease to make it 2-0 just before the interval.
Thiam smacked a shot wide after the restart as the Reds looked to get back into the contest before Brad Potts saw his effort crash back off the crossbar.
Sub Adam Hammill then pinged a shot just wide shortly after coming on before Craig Forsyth blazed over as Derby broke on the counter in search of a third.
They didn’t have to wait too long for the third though, as the impressive Weimann lashed home on 78 minutes to complete the rout.
For Paul Heckingbottom’s side, they now sit in 20th place and more worryingly they haven’t scored in open play for more than eight hours.
Heckingbottom bemoaned the difference in quality as his side slipped to a fifth consecutive defeat.
He said: “I have to give Derby credit, they were clinical.
“We didn’t take anything we made and we think we should do better with the goals. They were better than us.
“What our players are finding out is how tough this league is - we have to keep pushing and working. We just have to be consistent with them, pushing with them.
“We were less of a threat than Derby because they have the quality.
“When you’re playing against better opposition with more quality the things you are doing wrong will be punished.
“We all know what we’re playing for - we’re playing for points and positions. Hopefully before January we’ll have a few more wins.
“I know everything that has gone off at the club and I’m sat here at 3-0 down disappointed. I know the fans are, 100 per cent.
“I’d like to be realistic and understand the challenges facing everybody.”
Barnsley: Davies, McCarthy, Pearson, Lindsay, Yiadom, Potts (Hammill 60), Williams, Gardner (Moncur 61), Thiam (Ugbo 72), Barnes, Bradshaw
Subs not used: Townsend, Mallan, Fryers, McGeehan
Derby: Carson, Baird, Davies, Keogh, Forsyth, Lawrence (Russell 46), Ledley, Huddlestone, Weimann, Martin (Winnall 80), Vydra (Johnson 71)
Subs not used: Mitchell, Wisdom, Nugent, Thorne, Winnall
Ref: T Robinson (West Sussex).