Chelsea manager Jose Mourinho had warned prior to kick-off at Stamford Bridge that it would be a "disgrace" if his men were beaten.
But his words came back to haunt him as the League One team pulled off an upset that brought to mind their stunning run to the League Cup final in 2013.
Chelsea made nine changes to the team that had drawn 1-1 with Liverpool in Wednesday's League Cup semi-final first leg and took a 21st-minute lead when Gary Cahill flicked in Oscar's corner.
Ramires made it 2-0 in the 38th minute after a one-two with Mohamed Salah, but Jon Stead replied for Bradford three minutes later and former Chelsea youth player Filipe Morais equalised 15 minutes from time.
A money-spinning replay beckoned for the team who are currently seventh in the third tier, 51 places below Chelsea, but they went ahead in the 82nd minute when Andy Halliday found the top corner from 18 yards.
Mourinho introduced Willian, Cesc Fabregas and Eden Hazard from the bench, but it was Bradford who had the final say as substitute Mark Yeates calmly slotted home to claim his own piece of FA Cup folklore.
City manager Manuel Pellegrini was left to face questions about his side's midweek trip to Abu Dhabi for a warm-weather training camp after they were eliminated by Middlesbrough.
Currently second in the Championship, Middlesbrough weathered heavy pressure in the first half before capitalising on some farcical defending to take a 53rd-minute lead through on-loan Chelsea striker Patrick Bamford.
Fernando's back-pass sold Willy Caballero short and after the City goalkeeper collided with Albert Adomah, Fernando slid in to clear, only to play the ball against Bamford, whose touch took the ball in.
After Lee Tomlin had hit the post for Middlesbrough, with Frank Lampard replying in kind, substitute Kike secured victory for the visitors in stoppage time by finishing off a counter-attack led by Bamford.
City, who visit Chelsea in the league next weekend, have now lost successive home games for the first time in three years, having lost 2-0 at home to Arsenal last weekend.
- AAP