The Reds made it three consecutive Sky Bet Championship victories with a solid win at Ashton Gate.
A second half Carlton Morris strike was enough for Barnsley against a struggling Bristol City side this afternoon.
The big man's third goal in as many games sealed a first Reds victory at Ashton Gate in 28 years.
Head Coach, Valérien Ismaël had brought Daryl Dike and Michael Sollbauer back into his starting lineup for this one, with Finnish centre half Aapo Halme making a welcome return to the squad with a place on the bench as he makes his way back from injury.
The first half was dominated by the Reds, but clear-cut chances were few and far between. Of those few opportunities created, the visitors failed to make them count in the opening 45.
It was another blistering Reds start however, and inside the opening 10 minutes, Dike - who proved a handful again up front - looked to have been felled in the Robins' penalty area but the referee waved away any appeals for the foul. Replays suggested Mr James Linington made the correct call.
The lively Conor Chaplin, playing off the right flank fired off a fierce snapshot on the half-volley from just outside the box that warmed the hands of Robins goalkeeper Dan Bentley.
Soon afterwards, an inswinging Alex Mowatt corner looked to have curled straight into the net but the official spotted an infringement and awarded the home side a free-kick as a Robins defender hacked away from the goalline.
Barnsley's best chance of the first half came when Polish defender Michal Helik ghosted into the box, taking advantage of some slack defending and looked for all the world as though he'd fire into an empty net but his effort was skied over the bar. It was a head-in-hands moment for the usually lethal centre back.
Dike then stretched out a leg to try and divert a Mads Andersen header towards goal from a Mowatt free-kick but his hooked attempt comfortably cleared the crossbar.
The nearest 'moment' for Bristol City came in the closing stages of the half when a lack of communication at the back saw Andersen ignore his 'keeper's shouts and instead look to nod back a header to Brad Collins, but despite the Robins getting hold of the ball with the Reds defence all at sea, the hosts couldn't capitalise, summing up their wretched form of late.
HALF-TIME: Bristol City 0-0 Barnsley
The flow of the game was unmoved as we kicked off the second half, with an early chance for Chaplin just after the break when he saw a cute little flick towards goal well held by Bentley, after a fine cross by Callum Styles from the left-hand side.
On the opposite side, Callum Brittain then found his way into the box with some neat footwork but could also, only shoot straight at the goalkeeper from a central position, 10 yards from goal.
Ismaël had seen enough and went to his bench; the Frenchman made a triple change just before the hour-mark, withdrawing all of Woodrow, Chaplin and Styles, with Victor Adeboyejo, Carlton Morris and Jordan Williams entering the fray.
The Reds won the ball well in midfield on 65 minutes and Morris fed Brittain out wide on the right, but his low cross was stabbed clear with Reds bodies waiting to pounce. But the momentum was growing; the feeling was that a Barnsley goal was almost inevitable.
And indeed, the pressure paid off just two minutes later when Mowatt's latest corner kick was eventually slammed in by Morris from a yard out for his third goal in as many games, after Sollbauer had kept the ball alive at the far post. It was the most deserved goal you could imagine, such was the away side's dominance.
The captain, Mowatt then tried an ambitious effort from all of 35 yards but it flew over the bar. The Reds were pressing hard for that second goal.
Toby Sibbick joined the action on 75 minutes, replacing the impressive Sollbauer and he saw a close-range header fly just over the bar from another Mowatt free-kick.
The Robins never looked likely to hit back, and the Reds finished the game in control, to make it back-to-back away wins and move just five points from that 50-point marker set out by Ismaël three months ago.
FULL-TIME: Bristol City 0-1 Barnsley
Collins, Brittain, Sollbauer (Sibbick), Helik, Andersen, Styles (J.Williams), Mowatt, Palmer, Chaplin (Morris), Woodrow (Adeboyejo), Dike (Frieser).
Unused: Walton, Oduor, Halme, Kane.