First-half goals from Gary Cahill and Ramires looked to have put the Premier League leaders on course for a comfortable victory on Saturday, but League One promotion-hopefuls Bradford had other ideas.
Jonathan Stead pulled a goal back before the break and midfielder Filipe Morais, who left Chelsea during Jose Mourinho's first reign at the London club due to a lack of first-team football, equalised 15 minutes from time.
But there was yet more drama when Andy Halliday put Phil Parkinson's side in front in the 82nd minute, and Mark Yeates added a fourth in stoppage time to consign Chelsea to their first home defeat of the season, ending their hopes of winning the quadruple.
Mourinho named a much-changed side with a League Cup semi-final second leg against Liverpool and a crunch league clash with Manchester City to consider over the coming week and, despite bringing on Cesc Fabregas and Eden Hazard, he was unable to avoid an embarrassing defeat.
Teenage defender Andreas Christensen made only his second competitive start for Chelsea as Mourinho made nine changes to the side which drew at Liverpool in midweek, with Cahill and John Obi Mikel the only men to retain their places.
Experienced Bradford defender Andrew Davies was deemed fit enough to start, while striker Billy Clarke was on the bench after recovering from a knee injury.
Bradford were clearly not overawed by the occasion and Petr Cech produced an outstanding one-handed save to keep out Davies' header from a Morais corner after 14 minutes.
It was a corner at the other end which led to the opening goal seven minutes later, when Oscar swung the ball in and Cahill was on hand to flick in his second goal of the season from close range.
Didier Drogba almost doubled Chelsea's lead a couple of minutes later with a measured effort after a sharp turn, but Ben Williams denied the veteran striker with a fine save.
The hosts doubled their lead seven minutes before half-time, though, as Bradford lost possession on the halfway line and were made to pay by Ramires, who played a one-two with Mohamed Salah before seeing his shot go in off the post.
There appeared to be no way back for the League One side, but Stead pulled a goal back from out of the blue when he let fly with a venomous left-footed drive which Cech got a hand to but was unable to keep out just three minutes after Ramires' strike.
That was by no means a false dawn for Bradford, who started the second half on the front foot and Morais had a shot tipped over the crossbar by the alert Cech.
Billy Knott then tried his luck with a curled effort, but failed to work Cech, and Salah, who has been linked with a move to Roma, shot narrowly wide of the far post after 63 minutes as Chelsea strived to give themselves breathing space.
Chelsea were stunned when they failed to deal with a long throw from James Meredith, and Morais was on hand to side-foot home after Knott's shot was saved by Cech to send a huge away contingent into raptures.
Better was to come for the visitors, though, as Halliday found the top corner after Stead had laid the ball off and Yeates struck four minutes into time added on to seal one of the most sensational FA Cup upsets of all time.
