City were well beaten in South Yorkshire as fellow strugglers Sheffield United proved too strong on their own patch.
Goals from John Brayford, who opened the scoring just before half-time, Ryan Flynn and a Jose Baxter penalty condemned the Robins to a convincing defeat.
Steve Cotterill named the same team for the third game running, with Sam Baldock and Greg Cunningham continuing in unfamiliar wide midfield roles.
It was City who hit the first shot in anger inside the first two minutes. Wade Elliott, who famously scored the only goal of the Championship play-off final for Burnley against the Blades back in 2009, saw his fizzing effort from distance just bounce wide.
But from then on United began to take charge. Scottish winger Jamie Murphy beat City keeper Simon Moore to a high ball with a deft header which was trickling towards the net until Aden Flint intervened with a vital clearance.
Next to go close was Flynn, Murphy’s fellow wide man, whose low shot looked to be heading inside the far post only to curl away from goal at the last minute.
City were indebted to an unlikely defensive source for keeping their clean sheet intact when Jay Emmanuel-Thomas tracked back to make a crucial block on Harry Maguire after the United man charged out from the back and unleashed a ferocious drive.
It was a tricky opening period for City to negotiate, but, having come through it unscathed, the visitors began to stamp their authority on proceedings.
But for all their possession in a decent spell for the visitors midway through the second half, chances were not forthcoming.
Baldock latched on to Adam El-Abd’s ball over the top only to collide with United keeper Mark Howard, before the ball ran loose for Tyrone Barnett who was crowded out before he could get a shot away.
Just as the action looked to be petering out towards a half-time stalemate, the hosts struck at the best possible time, as Baxter’s corner was headed on by Maguire and lashed into the net by fellow defender Brayford from close range.
City needed a response after the interval but instead found themselves coming under more pressure from the home team, buoyed by scoring the opener.
Having threatened from a couple of set-pieces, the Blades unlocked the Robins from open play when Murphy burst down the left and picked out Flynn on the edge of the box, who took aim and dispatched a low shot into the bottom corner for number two.
City were in danger of being blown away as Conor Coady and the dangerous Flynn both came close to putting the result beyond doubt, before the goalscorer surged past Flint and invited Karleigh Osborne to lunge in and bring him down for a clear penalty.
Cotterill’s decision to make a double change – including bringing on Stephen Pearson for his first appearance of the season – did nothing to put off the impending spot-kick taker as Baxter beat Moore down to the keeper’s right with a convincing strike.
From then on City’s fate was sealed. Wes Burns was summoned from the bench and succeeded in worrying Ashton Gate old boy Matt Hill on a couple of occasions, but El-Abd’s sidefooted effort from Bobby Reid’s cross was the closest the visitors had come to dirtying Howard’s clean sheet.
That was until Elliott’s long-range shot was spilled by the keeper, allowing Baldock to steal in only to be denied by another save before Barnett fired the loose ball high into the stand.
All in all, a day to forget for Cotterill’s side.