Full-time score from The Den
In a real ding-dong affair Phil Parkinson's in-form Bantams took an early lead when Billy Knott slammed home the opening goal after Millwall had failed to clear their lines from a corner.
The Lions were not to be denied and their pressure paid off shortly when Scott McDonald steered a textbook header beyond Williams' reach and into the corner of the net after neat work on the wing by Lee Martin to level up nine minutes before the break.
Millwall kept knocking at the door and took a deserved lead in the 66th-minute when McDonald turned provider, picking out Fuller with a neat pass following a quick Lions counter-attack. Striker Fuller made no mistake with a crisp finish for his fourth goal of the season.
The visitors had their tails up and looked to have put one foot in the hat for Monday's Fourth Round draw just six minutes later when Knott expertly volleyed the ball in from close-range for his second goal of the game on 76 minutes.
Lions boss Ian Holloway introduced Magaye Gueye for Richard Chaplow with nine minutes remaining and the sub's first touch was a whisker away from picking out Fuller in the penalty area. His second delivery in the 83rd-minute, however, proved decisive as he did find Fuller, who coolly converted to level at 3-3.
Both teams had opportunities to grab a dramatic late winner, the best of which fell to Gueye, whose fierce 16-yard drive stung the hands of keeper Williams in the Bradford goal, meaning the two teams will meet again on Wednesday 14th January to see who goes through to Round Four.
Bookings: Upson (22mins), Chaplow (50mins)
Scorers: McDonald (36mins), Fuller (66, 83mins)
Booking: McArdle (53mins)
Scorers: Knott (6, 76mins), Nelson (70mins og)
Att: 5,470 (away 1,093)