Two goals in three minutes from substitute Marvin Elliott propelled City to three vital points at the expense of fellow strugglers Carlisle United.
The hosts were well below par throughout a first half which concluded with a single goal deficit inflicted by Brad Potts’ low free kick ten minutes before the interval.
But Steve Cotterill responded with a double switch at the break – one of whom proved to be the matchwinner, as Elliott attacked two corners in quick succession to maximum effect.
Manager Cotterill had shuffled his pack considerably before kick-off, making five changes to his side beaten 3-1 at league leaders Brentford in midweek.
The alterations included a debut for goalkeeper Simon Moore and a first start for Wade Elliott in midfield.
Elsewhere, Scott Wagstaff returned from a hamstring injury to replace Karleigh Osborne – sidelined by the same problem – while Jay Emmanuel-Thomas and Bobby Reid were also restored to the -starting line-up.
However, the theoretically fresher XI took a while to settle, best summed up by a dangerous pass across his own half by Derrick Williams pounced upon by Michael Drennan, who drove towards goal and hit a rasping shot from 25 yards which cannoned out off the angle of post and bar.
It was a wonderful strike deserving of a goal, with Moore unable to get anywhere near it.
Carlisle remained at ease defensively until the 20th minute, when Greg Cunningham’s nicely shaped cross invited a finish from Reid, but he was unable to make a substantial connection as the ball just brushed off his head and well wide of goal.
Slowly but surely City were showing signs of finding their rhythm, with Emmanuel-Thomas finding space to fire a right-footed shot across keeper Greg Fleming, who did well to make a sprawling save without parrying the ball out to a red shirt.
But ten minutes before the break, the Robins’ sluggishness was punished by the opening goal.
It started with a burst of pace from Carlisle debutant Charni Ekangamene to take him beyond Adam El-Abd, who responded by cynically blocking the run and fortunately avoiding a yellow card.
But that was not to be the end of the danger. From the resulting free kick, Potts’ low shot crept under the wall and caught out Moore at his near post.
Cotterill responded to the below par first half with a double change at the interval, replacing Elliott with his namesake Marvin and Williams with Wes Burns, as City switched to 4-4-2.
City took their time before raising their game, but Elliott showed a sign of things to come with a low shot from Sam Baldock’s lay-off which squirted away for a corner.
Then Burns raced to the byeline and found a cross which the visitors smuggled to safety.
But the home team, so often undone from set-pieces this season, turned the tide with two quickfire goals from corners of their own.
From the first of two Emmanuel-Thomas corners, Baldock retrieved the ball on the far side of the box and tossed it back into the danger zone for Elliott to plant a downward header back across Fleming and into the bottom corner.
Suddenly Ashton Gate was alive, and another Emmanuel-Thomas delivery was this time met on the full by Elliott, who sent a crashing volley high into the net from close range to complete a remarkable turnaround 20 minutes from time.
City had plenty of defending to do from there on in, but keeper Moore was relatively untested as a succession of corners came and went for the visitors, who were probably left wondering quite how they had lost the game.