Jay Tabb started for Reading at the Madejski Stadium but visitors Burnley who led 1-0 from the first leg thanks to a penalty from Cov kid Graham Alexander, took the lead in the 51st minute.
It was a stunning goal from Martin Patterson who raced from his own half before hitting a thrity yarder past Marcus Hahneman.
Steve Coppell made a triple substitution but his side went further behind in the 58th minute when a dipping volley from Steve Thompson went into the net to delight the travelling support.
Burnley's game against Sheffield United will be played at Wembley on Monday May 25th.