City were fortunate to escape with maximum points at home to a Notts County side who showed all the fight of a team battling for their Sky Bet League One lives at Ashton Gate.
It was the Robins who took an early lead through Sam Baldock’s 22nd league goal of the season, despite being on the back foot in the opening exchanges.
It was a pattern that continued long after Haydn Hollis headed the visitors level just before the half-hour mark.
But, try as they might, County could not breach City’s Simon Moore for a second time in search of three vital points in the race for survival.
Instead, they shot themselves in the foot when keeper Bartosz Bialkowski’s air kick allowed Baldock to snatch victory with four minutes to go.
Steve Cotterill named an unchanged side following last weekend’s 1-0 away victory at Walsall.
Returning midfielder Simon Gillett, available again after a two-game ban, missed out on a place in the squad as the unlucky sixth loan player, with Cotterill only permitted to include a maximum of five.
The relegation-threatened visitors started full of intent, forcing a handful of early corners, but it was City who enjoyed the first notable goalscoring chance.
Baldock raced on to a long ball forward, ran clear of defender Hollis to reach the byeline and cut the ball back for strike partner Martin Paterson, who could only send his shot over the crossbar from 12 yards.
At the other end, it was left-winger Jack Grealish who was causing most of the problems for the Robins defensively, breezing past Nyron Nosworthy to set up Ronan Murray whose shot was excellently blocked by Karleigh Osborne.
But City’s superior firepower would contrive to edge them in front inside 13 minutes.
Paterson, having dropped out to the left flank, found a low cross that did not look the most threatening until Baldock nipped in front of his man just in time to prod the ball home from close range.
However, the goal did nothing to put County off their stride.
Murray’s teasing centre was only just too long for a team-mate to convert, before left-back Alan Sheehan twice tried his luck from distance.
First, his 30-yard free kick looked goalbound until Derrick Williams’ header helped it on its way behind, before a rasping drive from even further out needed tipping around the near post by Moore.
From the resulting corner, Sheehan’s clipped delivery was met by a towering leap from Hollis to level the scores on 29 minutes – an equaliser nobody could argue was against the run of play.
After having their wings clipped by the leveller, the Robins were roused in the latter stages of the first half, summed up by a delicious diagonal pass from Marlon Pack taken brilliantly in his stride by Baldock who was only denied by a sprawling save.
Cotterill responded to a sluggish display from his side with a half-time change, introducing Brendan Moloney for the booked Greg Cunningham with Derrick Williams switching to the left flank.
But City would continue to struggle to stem the flow, even after Paterson sidefooted high and wide when the ball kindly rolled his way soon after the break.
Sheehan remained a problem with his set-piece delivery, with one driven cross headed over from close range by Hollis in front of Moore, who had to save his own blushes four minutes later.
After some neat hold-up play from Jimmy Spencer, the striker’s eventual shot resembled more of a backpass before taking an alarming bobble to deceive Moore, who only just redeemed himself in the nick of time to claw the ball out with Gary Liddle sliding in.
City had not been themselves at all, and County were pushing harder for what would be a priceless winner in their quest to avoid the drop.
Even the introduction of Wes Burns did little to inject any life into the hosts, as Liddle’s rising drive only just cleared the crossbar before County replacement Callum McGregor was denied by a stopping save from Moore down to his left.
Grealish also went close, sidefooting wide from the edge of the box, before Bialkowski’s howler presented Baldock with the match-winning chance and league goal number 23 of his career-best campaign.