A goal in either half sees the Reds take the spoils in the Yorkshire derby!
A first half header from Tom Bradshaw was followed up by a second half goal for Victor Adeboyejo in the Yorkshire derby as hosts Bradford City were seen off comfortably at Valley Parade.
Daniel Stendel had named an unchanged lineup from last weekend's opening day victory over Oxford United at Oakwell and again his side got off to the perfect start.
After Kieffer Moore had been denied twice inside the box by Bantams 'keeper Richard O'Donnell, it was his strike partner who struck the first blow seconds later.
A terrific first-time cross from Dimitri Cavaré from the right was met by the flying head of Tom Bradshaw, a bullet of a connection and O'Donnell had no chance of preventing the ball from finding the corner of his net to give Barnsley a seventh minute lead.
Within five minutes it was nearly two - Liam Lindsay rising highest at the far post to meet Alex Mowatt's corner but the Scotsman's header was clawed away and over the bar by the busy O'Donnell.
It was incessant Reds pressure, no room given to Bradford to even think about getting their own game going.
After 20 or so minutes the game settled a little with the home side eventually seeing more of the ball and on the half hour they had their first real opportunity.
Ethan Pinnock was fouled 30 yards from his own goal, the referee waved play on and Eoin Doyle broke clear and into the box right hand side, he crossed low and hard, Cavaré tried to divert it only to fire it straight at Adam Davies who reacted superbly to claim the bouncing ball.
With a couple of minutes remaining in the first half the Reds hit Bradford on the counter in sublime fashion with only the finish missing at the end of it.
Mowatt and Kenny Dougall closed their man down, nicked it, Pinnock stepped in and played a sumptuous pass 50 yards towards Mamadou Thiam out wide left; the Senegalese tricked his full back, cut inside onto his right boot and let fly from 25 yards, but the effort bent just wide of the far post.
It had been a bossy first half performance from Stendel's side, but only a slender lead to show for it.
HALF TIME: Bradford City 0-1 Barnsley
Joe Riley made way for Sherwin Seedorf at the break as the hosts looked to find a way back into the match.
But it was nearly 2-0 within seconds of the restart as Mowatt tried his luck from 25 yards out, forcing O'Donnell to turn the ball behind for another Barnsley corner.
The game became scrappier for a good 15 minutes, with the Bantams beginning to find their rhythm a little.
There was nothing really threatening created by the home side during their better spell however, and Davies was untested throughout the second half.
Stendel however, had seen enough of this and in looking to get his charges back into the ascendance he decided to bring on George Moncur and Victor Adeboyejo, replacing Thiam and Moore, the latter had picked up a knock just prior.
Three minutes later and that decision proved inspired.
Bradshaw won the ball at left back - he'd put in an epic shift - before floating a ball up to Adeboyejo. Young Victor outmuscled his defender, laid it off to the fast sprinting Moncur who dribbled beyond three men, got to the byline and shot low and hard, the 'keeper couldn't keep it from heading towards goal but Adeboyejo was on hand, Johnny on the spot to tap in regardless.
Moncur had a couple of efforts from range that didn't test O'Donnell but the game petered out somewhat with Barnsley keeping possession and managing the game well.
There was one last opportunity for Barnsley; Mowatt's vicious inswinging corner was met by Bradshaw's head, but fortunately for the hosts it was straight at O'Donnell who did brilliantly to divert it over the bar.
Late bookings for Dani Pinillos and Cavaré didn't take the shine off what was a great day out just up the road, as Stendel's side made it two wins - with two clean sheets - from their opening two matches.
Onto Blackpool and the Carabao Cup!
FULL TIME: Bradford City 0-2 Barnsley
Reds: Davies (GK), Cavaré, Pinnock, Lindsay, Pinillos, Potts (Isgrove '88), Mowatt, Dougall, Thiam (Moncur '67), Moore (Adeboyejo '67), Bradshaw.
Unused: Walton (GK), J.Williams, McGeehan, Jackson.
Att: 18,986 (2,552 Reds)