The Championship side made a blistering start to Monday's quarter-final replay and booked a trip to Wembley through Robson-Kanu's header and McCleary's deflected strike inside the opening nine minutes.
Jamie Mackie added a third midway through the second period following Filipe Morais' straight red card just after the hour mark for clattering a high boot into Nathaniel Chalobah's midriff to further compound Bradford's woes.
Bradford – who dumped out Premier League sides Chelsea and Sunderland to reach the last eight – never recovered from the early blitz as it proved a game too far in a competition that Phil Parkinson's men have injected some much-needed magic this season.
While Parkinson turns his attention to securing Bradford a League One play-off berth, Reading counterpart Steve Clarke was left to bask in steering the Berkshire club to their first FA Cup semi-final since 1927.
Clarke, an FA Cup winner during his playing days at Chelsea, fielded an entirely different XI to the team that lost 4-1 at Watford on Saturday, but any fears from home fans that Reading may take time to gel were quickly extinguished.
Robson-Kanu broke the deadlock when he timed his run to perfection to get ahead of Stephen Darby and glance a six-yard header across Ben Williams after meeting McCleary's inswinging corner at the near post.
McCleary then doubled Reading's advantage three minutes later in rather fortuitous circumstances to leave Bradford shell-shocked.
The Jamaica international cut in from the right, worked some space for himself with some quick footwork before hitting a shot that clipped Andy Halliday and looped over the goalkeeper.
Ben Williams reacted sharply to palm away a swerving 25-yard Danny Williams effort as the hosts went in search of a third and McCleary created a carbon-copy of the build-up play that led to his earlier goal, but curled well over.
Any slim hopes of a Bradford fightback disappeared when Morais saw red for his rash challenge on Chalobah, who then picked himself up to set up Mackie's fifth goal in his last six games with 22 minutes remaining.
Chalobah slipped the ball through for Mackie to beat the offside trap and drill between Ben Williams' legs to send the home supporters into raptures.
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