Bradford’s fairytale run was brought to an end as Reading sealed their first FA Cup semi-final appearance for 88 years.
A Hal Robson-Kanu header and deflected Garath McCleary shot in the opening nine minutes set the Championship side on the way to a sixth-round replay win.
Bradford’s Filipe Morais was sent off for a high challenge on 63 minutes and Jamie Mackie scored Reading’s third shortly after with a neat low finish.
The Royals will face FA Cup holders Arsenal at Wembley on 18 or 19 April.
Reading took control straight from the first whistle, nine days after the sides battled out a 0-0 stalemate at Valley Parade.
Robson-Kanu gave them an ideal start, rising to score with a near-post header from McCleary’s sixth-minute corner.
The impressive McCleary – later the alleged victim of racist abuse by a supporter – doubled the lead three minutes later with Phil Parkinson’s side still attempting to regroup.
The winger cut in from the right to beat keeper Ben Williams from just inside the area with a shot that took a big looping deflection off Andy Halliday.
A fine save from Williams prevented Reading’s Dan Williams from adding a long-range third before half-time.
League One Bradford, who made six changes to the side that drew with Notts County on Saturday, retained hope of a second-half comeback, after recovering from two goals down in round four to beat Chelsea 4-2 at Stamford Bridge in one of the competition’s greatest-ever shocks.
But 48 hours after their last game, the tired-looking Bantams never appeared capable of a repeat of their heroics, which had also seen them knock out Premier League Sunderland and Championship side Millwallduring a memorable run.
Their task was made even harder when Morais was shown a straight red card for a high challenge on Nathaniel Chalobah – the Portuguese winger’s foot connecting with the on-loan Chelsea midfielder’s midriff as they contested a high ball.
Reading, who had rested all of their starting 11 in Saturday’s 4-1 defeat by Watford, pressed home their numerical advantage, Chalobah releasing Mackie to fire past an exposed Williams.
Home fans celebrated on the pitch after the final whistle, having had time to savour the success in a one-sided contest.