The two sides shared a goalless draw in the original tie at Valley Parade but Reading were the better side in Monday's replay, sealing a comfortable 3-0 win to reach their first semi-final since 1927.
Bradford have made a name for themselves as giant killers in recent years, and had knocked out two Premier League sides on their way to this season's last eight, but they could not work their way back into this game and will now return to fighting for promotion from League One.
The kick-off time was almost altered as Bradford supporters fought against heavy traffic, but those away fans who did get in on time only witnessed their team struggle to get out of first gear.
Reading, meanwhile, looked fresh as Steve Clarke made 11 changes from the side that lost 4-1 to Watford in the Championship on Saturday.
Hal Robson-Kanu's header put the Royals in front with the game's first chance and the impressive Garath McCleary saw a shot deflected in on nine minutes meaning Bradford would requite another historical evening to seal another trip to Wembley.
Any hope the Bantams had of completing a comeback was made more difficult when Felipe Morais was shown a straight red card for a high foot on Nathaniel Chalobah just after the hour-mark.
And it was Chelsea loanee Chalobah who set-up the third Reading goal which truly put the game beyond doubt as he fed Jamie Mackie - who hammered home a third for the hosts.
It was Mackie who charged into the area and his run was only halted by a strong challenge from Bantams' skipper Stephen Darby.
The resulting corner was whipped in by McCleary and Robson-Kanu was on hand to head Reading in front with six minutes on the clock.
James Hanson then headed straight at Adam Federici as Bradford looked to level the tie immediately and they were soon made to pay for starting the game sluggishly.
McCleary was tormenting Bradford and he put the tie firmly in Reading's hands as he cut inside before hitting a shot that ballooned off of Andy Halliday and looped over Ben Williams to double the hosts' lead.
Bradford famously recovered from 2-0 down to seal a remarkable fourth-round victory over Chelsea at Stamford Bridge but they had Williams to thank for keeping them in the game as he pushed away a speculative Danny Williams drive with Clarke's side pushing to kill the tie early on.
The rest of the first half proved to be a much more even affair, but still Reading created the better openings and McCleary should have done better with a chance before the break but could only fire high and wide when well-placed.
Federici was called into action on the stroke of half-time as Billy Knott could not make the best of a Bradford breakaway.
The second half started without the same fanfare as the first as Reading looked to complete a professional job and Bradford toiled to get a foothold on the game.
The first incident of note came when Morais was dismissed for catching Chalobah with a high foot as the two looked to win a long ball - with referee Mike Jones originally pulling out a yellow card before deciding the former Chelsea youngster's challenge was worthy of a straight red.
The game was then killed off by Mackie, who timed his run to perfection to latch onto Chalobah's through ball and thrash an effort past Williams to send Reading into only the second FA Cup semi-final in the club's 144-year history, with the home fans running on to celebrate on the pitch at full-time.
Source : PA