Barnsley manager Simon Davey is looking to a South Yorkshire derby at Hillsborough to halt a worrying slide towards the Championship relegation zone.
The Tykes make the short trek over the M1 to tackle Sheffield Wednesday still smarting from a 2-0 defeat at Ashton Gate.
Second-half goals from substitute Gavin Williams and Michael McIndoe made it four wins and a draw from Bristol's last five Championship fixtures.
Between the goals, City goalkeeper Adriano Basso made an outstanding fingertip save to divert Bobby Hassell strike on to the crossbar.
Barnsley boss Davey was left hugely frustrated after seeing his side sit just two points above third-from-bottom Watford in the Championship.
"For an hour we were well in the game and created the better chances," he said.
"But then we switched off and I was disappointed with the defending for their first goal.
"We're on a poor run and need to end it on Tuesday night at home to Sheffield Wednesday. There will be Yorkshire pride at stake and I'm sure that will inspire the players.
"This was an improved performance and but for a fantastic save by their keeper we would have equalised. It's something to build on."
City also hit the woodwork after 57 minutes when Bradley Orr arrived at the far post to meet McIndoe's cross and hammered the ball against the crossbar.
Gary Johnson is more convinced than ever his City team can mount a charge towards the play-offs.
"We're in good form and confidence is high so hopefully we can continue to make ground on the clubs above us," he said.
"Back-to-back home matches is an ideal opportunity to do that and we will be looking for three more points on Tuesday.
"I knew this would be a game in which we needed to show patience because Barnsley were always going to get men behind the ball. They also have players who can break on you so it's dangerous to over-commit.
"We kept our composure and eventually scored two superbly taken goals. By the closing stages we were dominating and everyone was looking comfortable on the ball."
Williams capitalised on a brilliant through ball from Cole Skuse to fire past Heinz Muller in the 66th minute after Barnsley had looked more likely to break the deadlock.
Thereafter the home side took control and McIndoe sealed the result 11 minutes from time, shooting powerfully home after Peter Styvar's effort had been blocked.
Bristol City: Basso, Orr, Carey, Fontaine, McAllister, Skuse, Johnson, McIndoe, Sproule (Williams 54), Adebola (Akinde 82), John (Styvar 54). Unused substitutes: Henderson, Iriekpen.
Barnsley: Muller, Van Homoet, Moore, Guedes, Kozluk, Campbell-Ryce, Hassell, De Silva, Devaney, Odejayi, Macken. Unused substitutes: Steele, El Haimour, Butterfield, Potter, Heslop.
Referee: T Kettle (Rutland).
Man of the match: Michael McIndoe.