Stephen Darby's stunning late strike gave City a dramatic victory in Extra Time over fellow League 2 outfit Burton Albion, to book their place in Wednesday night's 4th round draw and have a great chance of coming up against a Premier League side in the next stage.
City dominated early on and Stuart Tomlinson was looking nervy in the wet conditions, spilling firm shots from both Gary Jones and Alan Connell.
Garry Thompson drilled a shot narrowly wide of the target from an angle on the edge of the area as The Bantams pressed for an early goal.
Against the run of play, Burton went ahead; Lee Bell sprayed a ball out wide to Jack Dyer, Dyer's cross was asking to be hit and Billy Kee ran onto it to smash the ball in from 12 yards past a helpless Matt Duke.
Soon after, Zavon Hines almost produced a stunning equaliser; good build up play allowed the winger to shoot goalwards, a smart save from Tomlinson denied him.
On the 29th minute, the visitors doubled their advantage. Lee Bell's deflected shot forced a corner and from the resulting set piece Aaron Webster headed goalwards; Jones appeared to clear on the goal line, but the linesman flagged to correctly award the goal.
Garry Thompson was sent through on goal by a Hines pass but as he tried to round Tomlinson, Burton bodies got behind the ball and Thompson's shot squirmed harmlessly across goal.
On the stroke of half time McArdle headed a Hines cross towards the bottom corner of the goal to force Stuart Tomlinson into a very good save.
Early on in the second half, Gary Jones was inches away from scoring a stunning freekick after Ricky Ravenhill had been brought down 20 yards from goal. Alan Connell thought he had won his side a penalty moments later when he was bundled over in the area, much to the frustration of the home crowd though he was booked for simulation.
Phil Parkinson went all out for a comeback making a triple substitution on the hour, replacing Ravenhill, Connell and Hines with Reid, Hanson and Wells.
Kyel Reid tried his luck with a freekick that flew a yard or so over the bar after Wells had been bundled over.
The subs were making an obvious difference to the game and Wells almost pulled a goal back when he lashed a shot narrowly over from an angle after Hanson's flick had released him.
Kyel Reid was near his best after coming on and nearly always had the beating of both Andrew Corbett and Cleveland Taylor at the same time.
On the 83rd minute Nahki Wells scored to give City a glimmer of hope; Meredith had good vision to pick him out and he turned to emphatically blast the ball across the keeper and into the top corner.
Sub Matt Paterson almost sealed the victory when he raced through alone, out pacing Meredith and McArdle, but Duke was on hand to make a brilliant low save.
Into the last minute of the game Nahki Wells equalised; Hanson's overhead kick, after a scramble in the 18 yard box, was poked home off the inside of the post by The Bermudian to send the game to Extra Time.
Early on in the first half of extra time, Matt Paterson gets minimal contact on the ball from a cross to send the ball rolling narrowly wide of Duke's post.
Moments later Hanson links up well with Wells once again, the big man's knock down was lashed narrowly over by the Night's super sub.
Into the second period of Extra Time and Cleveland Taylor was next to try his luck with a powerful, curling shot that zipped comfortably wide.
An inviting Stephen Darby cross was headed narrowly wide by Hanson, but moments later with the game looking set to head to penalties, the former Liverpool man set his sights from 25 yards and his low shot fizzed beyond the reach of Tomlinson and Into the bottom corner to send City through to the 4th round.