Jay Emmanuel-Thomas struck a goal in each half to book City a home tie with Premier League side West Ham United in the FA Cup fourth round.
Steve Cotterill’s team were never at their fluent best and had work to do in preserving a second successive clean sheet against away specialists Doncaster Rovers.
But ultimately Emmanuel-Thomas’ untidy 36th minute opener and far more typically stylish second 11 minutes from time were sufficient to earn City a crack at top-flight opponents in reaching round four for the first time in eight years.
Manager Cotterill made three changes to his side following the comprehensive 4-0 victory over Notts County in league action last time out.
Greg Cunningham was recalled at left wing-back at the expense of Joe Bryan, while Marlon Pack and Scott Wagstaff started in a three-man midfield with Wade Elliott and Luke Freeman among the substitutes.
Bobby Reid was forced to sit out the clash due to FA rules, having been unavailable for the original tie at the Keepmoat Stadium ten days prior when on loan at Plymouth Argyle.
It was a strangely subdued start to the contest in front of only two populated stands, with little to report in the opening exchanges.
Matt Smith, scorer of the equaliser in South Yorkshire to earn a replay, was the target for an early Greg Cunningham cross but unable to generate the necessary power to trouble Marko Marosi in the visiting goal.
Marosi, a Slovakia Under-21 international, was making the first start of his career.
Meanwhile, Doncaster were showing flashes of their counter-attacking threat, particularly through lone striker Curtis Main.
It was Main who raced to the byeline to supply a cross inviting to be struck on the volley by James Coppinger, who could only scuff his shot into the turf.
City would create the best chance to date on 18 minutes, as Emmanuel-Thomas cleverly hooked the ball over his shoulder to release the run of Wagstaff from midfield.
But with only Marosi to beat, the midfielder’s attempted lob from long range was rushed and drifted a long way wide of the target.
Slowly but surely the hosts were beginning to click into gear. Mark Little hit a low shot into the gloves of Marosi before Aden Flint met a right-wing corner from Pack with a thunderous header which flew just over the top.
Flint was to become an increasing menace to the visitors, trying his luck on the half-volley from 20 yards from Smith’s knockdown before playing a key role in the opening goal.
It was a move started by what looked a well overhit crossfield pass from Pack, only for Little to pluck the ball out of the air with a sublime first touch before embarking on a driving run to the byeline and producing a low cross which looked destined to be converted by Smith but Rovers somehow survived.
Instead City would force a corner, from which Flint met Pack’s delivery with a downward header scrambled away by Marosi back into the path of the defender.
When Flint’s follow-up shot was deflected and looped into the air, Emmanuel-Thomas was on hand to head home from virtually on the goal line in uncharacteristically messy fashion.
City were on their way to a fourth round date with Premier League opposition, but Donny threw caution to the wind in the first half’s closing stages.
First Coppinger checked inside and beat Frank Fielding with a seemingly unstoppable shot destined for the top corner only for the covering Little to head the ball clear from his own goal line.
Then left-back Enda Stevens caught a low drive sweetly in added time which escaped Fielding’s grasp as the home faithful breathed a sigh of relief for the second time in quick succession.
The interval seemed to have come at a good time for the hosts, who resumed the game looking much sharper.
Emmanuel-Thomas continued to be at the heart of everything that was good about City’s attacking play, floating a free kick on to the head of Pack before whipping a very different cross in towards Smith, who could use the pace on the ball to guide a header only a fraction wide of the upright.
But Doncaster would continue to have their moments, as Fielding had to be alert to keep out Paul Keegan before Harry Middleton skied the rebound.
Suddenly City had defending to do as Rovers’ boss Paul Dickov introduced two additional strikers from the bench in the shape of Theo Robinson and Nathan Tyson.
Plenty of Doncaster pressure ensued before Emmanuel-Thomas doubled his tally for the night to finally put the tie to bed.
With the visitors overcommitting men forward, Pack profited to lead a City breakaway 11 minutes from the end, opting to supply Emmanuel-Thomas to his right.
In typically composed fashion, the frontman twice faked to shoot and twice left defenders in his wake before stroking in the killer second on his trusty left foot.
After the final whistle City had to wait a further 45 minutes to discover their fourth round opponents, with West Ham requiring extra time and a penalty shoot-out to overcome top-flight rivals Everton and book their trip to Ashton Gate on Sunday, January 25th.