A controversial penalty awarded to Robins’s side proved crucial in their 4-2 triumph, referee Nigel Miller pointing to the spot with 32 minutes on the clock after he adjudged Marvin Elliott to have handled.
Andy Gray duly dispatched the kick, cancelling out Elliott’s sixth-minute opener, before Danny Haynes and Jacob Butterfield put the home side 3-1 ahead at the break.
Paul McShane completed the scoring for the hosts shortly after the restart before Nicky Maynard struck a late penalty to cut the arrears.
While the south Yorkshire club are safe in mid-table, their manager wants them to build on Saturday’s impressive win in the final six games of the season.
QPR await tomorrow, but Robins looked to relegation-threatened Scunthorpe’s 4-1 hammering of the league leaders for inspiration as his side seek to swiftly add to their 50 points.
He said: “We’ve got 18 more points to play for and at this moment I think 68 is achievable.
“After you win you think you can conquer the world and as long as you work hard you’re going to get your rewards.
“Next we’ve got to emulate Scunthorpe and beat QPR on Tuesday night.
“I thought the atmosphere at the ground today was good and I want us to play attacking football.”
City boss Keith Millen felt the controversial penalty turned the tide of the match against his side – and criticised the officials for their handling of the incident.
He said: “It’s hit Marvin on the side of the hip and that’s what annoyed the players.”
Barnsley: Steele, Trippier (Arismendi 80), McShane, Foster, Hill, Haynes, Doyle, Colace (Mellis 24), Butterfield, Harewood, Gray (Noble-Lazarus 90). Unused substitutes: Preece, McEveley, O’Brien, Clark.
Bristol City: James, Spence, Cisse, Nyatanga, McAllister (Woolford 78), Elliott, Johnson (Skuse 60), Campbell-Ryce, Adomah, Maynard, Pitman (Clarkson 61). Unused substitutes: Gerken, Wilson, Edwards, Stead.
Referee: N Miller (Durham).
Tykes man-of-the-match: Danny Haynes.