The final will be the Clarets' 61st match of a long and adventurous season that saw them come within minutes of Wembley in the Carling Cup.
Reading are left to reflect on a campaign that at one point suggested an immediate return to the Premier League but floundered on a dramatic loss of form at home over the closing months of the season.
It might have been a different story had the home team translated their early dominance of the match into an opening goal but, as was the case in the first leg, they could find no way past Brian Jensen.
Reading, with 20-year-old striker Simon Church making his first start for the club, played with a high tempo from the opening whistle, taking the game to their opponents, but Steve Coppell's men had to wait 15 minutes before finally testing the Clarets keeper.
The Dane parried a crisp strike from Shane Long after a corner was flicked into the striker's path at the far post, while Michael Duberry blazed over with the rebound.
Thompson (left) scored the second goal, a looping volley
Long's was the only clear chance of an opening period in which Reading pressed and probed, with Marek Matejovsky pulling the strings in midfield, while the Clarets saw little of the ball - particularly attacking players like Robbie Blake and Wade Elliott.
However, Elliott made a crisp connection from Chris McCann's cross after 25 minutes and the ball took a slight deflection off a Royals player before narrowly missing Hahnemann's goal.
Reading went on to create the bulk of the precious few chances served up in the remainder of the opening half, including a low free-kick from Dan Harding that was well saved by Jensen.
The keeper must have been unsighted after the ball flew under the wall, which to a man had leapt in the air, but he got down well to block the strike and then scooped it up before an opposition player could pounce on the rebound.
The match continued in a tight and tense fashion after the break before Paterson's searing left-foot strike left the Royals needing two goals to take the tie into extra-time.
Paterson was gifted far too much space to drift in from the right flank before smashing the ball past Hahnemann.
Coppell responded decisively, introducing Dave Kitson, Stephen Hunt and Glen Little for Matejovsky, Jimmy Kebe and Church in a bold triple substitution.
However, before the trio could impact upon the game Thompson stunned the home supporters with his audacious left-foot strike.
Reading had further chances but neither Long nor Kitson could find the target and Burnley closed out the match to seal their place in the final.
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