Paul Heckingbottom’s men showed class and guile in equal measure as they saw off Derby’s disappointing challenge.
It was a rather cagy opening period at Oakwell as the Reds scored the only goal and restricted Nigel Pearson’s Derby to strikes from distance.
The hosts struck first after just 11 minutes, though there was an element of luck about the goal.
The recalled Ryan Kent touched the ball to Conor Hourihane, and as his piledriver from 25 yards intially struck the base of a post, it bounced back, struck Rams ‘keeper Scott Carson and trickled into the goal.
It was a perfect start for the Reds, but Josh Scowen could have doubled the lead.
The Rams responded with Craig Bryson firing disappointingly wide, while Reds defender Alfie Mawson had to be at his brilliant best to thwart the on-rushing Darren Bent.
Tom Ince fired over wastefully for Derby as the game entered first-half stoppage-time.
The Reds doubled their lead just three minutes after the restart.
There was no luck involved this time as Mawson rose highest to glance home Hourihane’s in-swinging free-kick.
It was almost 3-0 minutes later. This time Carson produced a brilliant acrobatic save to palm away Hourihane’s crisply-struck volley.
Youngster Kent then came close to opening his Barnsley account, pouncing on a loose ball before crashing a shot against the post.
Adam Davies came to Barnsley’s rescue late on, saving brilliantly from Craig Forsyth and Johnny Russell.
Barnsley (4-4-2): Davies; Bree, Roberts, Mawson, White; Hammill (Lee, 90), Scowen, Hourihane, Kent; Bradshaw (Payne, 72), Watkins (D’Almeida, 90). Subs not used: Townsend, Yiadom, MacDonald, Moncur.
Derby (4-4-1-1): Carson; Forsyth, Shackell, Keogh, Christie; Butterfield (Russell, 55), Bryson, Hendrick (Hughes, 12), Blackman; Ince; Bent (Martin, 46). Subs not used: Grant, Pearce, Johnson, Baird.
Referee: Tony Harrington (Cleveland).