An early strike from former Manchester United youngster David Jones and a Matt Oakley second-half effort put the result beyond strugglers Barnsley, who had keeper David Lucas stretchered off and scored an injury-time consolation goal.
Derby were hampered by the absence of 17-goal leading scorer Steve Howard but made light of the loss as the swept into an 11th minute lead.
Giles Barnes smashed a close-range shot but was denied by a super reflex save from keeper Lucas, but Jones finished off with an emphatic shot from ten yards as Barnsley were slow to react.
Derby might have stretched their advantage after 25 minutes when a quick break from the back saw Darren Currie curl in a low cross behind the defence aimed at Jon Macken but Antony Kay stretched to intercept.
Another opportunity came Derby's way when Jones crossed after a short corner but Dean Leacock's towering header was high.
Midfielder Kyel Reid carved out an opening at the other end when he cut inside but his wind-assisted shot from 25 yards drifted over.
And when Derby conceded a free-kick in a dangerous spot, Brian Howard crashed it over the top before a Howard shot set up Hungary international Peter Rajczi but he was robbed as he tried to turn.
But the visitors added a second four minutes into the second half and suffered a double blow with the loss of Lucas.
Lucas, making his first start for the club, charged off his line in an ambitious attempt to punch away a free-kick from his opposite number.
He clattered into Barnsley defender Paul Reid and Derby's Barnes and crashed to the ground awkwardly as the ball dropped for Oakley, who drilled in his shot from the edge of the area.
After a worrying seven minutes sprawled on the ground receiving treatment, Lucas was stretchered away unconscious and being given oxygen, but he recovered consciousness on the way to hospital.
Barnsley immediately reshaped to an orthodox 4-4-2 in a bid to find a way back but Derby - cheered on by a 7,400 following - rarely looked troubled.
But the home side finally grabbed a consolation seven minutes into stoppage time when Sam Togwell hit an angled shot past Stephen Bywater.