A glaring error by goalkeeper Luke Steele allowed Jeff Hendrick to put the Rams ahead before a deflected Johnny Russell shot increased their lead and, although Nick Proschwitz pulled a goal back, it came too late for the visitors.
Russell had a chance to extend the hosts’ advantage with a penalty eight minutes from the end, but saw it saved by Steele.
Barnsley knew they needed a top performance against a team that had scored 11 goals in their previous three home games, but it was all Derby in the opening 10 minutes with Hendrick curling a shot just over from the edge of the box.
Chris Martin headed over after ex-Derby defender Lewin Nyatanga had given the ball away, but another former Rams player Tomasz Cywka forced Lee Grant into a diving save in the 17th minute in a rare Barnsley attack.
The pressure was soon back on the visitors, who were cut open by a quick one-two between Jamie Ward and Russell in the 21st minute only for the Scot to side-foot wide from 10 yards.
Derby’s passing and movement had caused problems from the start, but it was a mistake by Steele that gifted the home side a 34th-minute lead when the goalkeeper thought a 25-yard shot from Hendrick was going wide only for the ball to creep inside his right post.
It was the last thing Barnsley could afford, but Steele was blameless for the second goal in the 42nd minute when Russell’s 22-yard strike took a big deflection off the back of team-mate Craig Bryson and looped just under the bar.
Barnsley had to get back in the game as quickly as possible and they started the second half encouragingly when Tom Kennedy’s 20-yard free-kick was touched over by Grant.
Some of the fluency had gone out of Derby’s game but Barnsley lacked the quality to take advantage and Craig Forsyth was close to increasing the lead when he fired just over after a strong run down the left.
Bryson curled a 20-yard free-kick narrowly over with Steele at full stretch and Derby went close again in the 78th minute when substitute Simon Dawkins lifted the ball over the goalkeeper and Forsyth’s header was cleared off the line by Nyatanga.
But Barnsley were back in it with 10 minutes to go when Nyatanga played the ball in for Proschwitz to slide a low shot past Grant from 12 yards and Steele kept his side in it two minutes later when he saved a Russell penalty after Conor Sammon had been tripped by Jean Yves Mvoto.
Steele saved another effort from Bryson in the closing stages to keep the Barnsley fans optimistic of getting something out of the game, but their last hope vanished when Proschwitz was too high with a free-kick from 20 yards in the 88th minute.