Both their goals came after the interval in a game which went Reading's way before the break, without the Royals being able to score. It was the ninth successive home game in which Reading had failed to win, a run which proved their downfall.
Burnley struck the first blow six minutes into the second half with the opening goal of this leg. Martin Paterson collected the ball just inside his own half and ran on totally unchallenged until shooting past Marcus Hahnemann from around 25 yards out.
Seven minutes later they hit the second and clinching goal as Steve Thompson fired another effort past Hahnemann from the edge of the penalty area after a long clearance by Brian Jensen. They were two stunning goals and at that stage Reading knew their season was over.
Reading's response to Burnley's opener had been to put all three substitutes on in an all-out effort to get back in the game. When the second goal went in there was nothing left for Steve Coppell to try.
The home side sprung a surprise by giving a first league start to young striker Simon Church, who has spent most of the season on loan at Wycombe and Leyton Orient and it was the Royals who generated the better chances early on.
Shane Long tested Brian Jensen with a shot which the keeper blocked and when the ball rebounded to Reading skipper Michael Duberry. he fired it over the Clarets bar.
There was a fright for Reading in the 25th minute when a shot by Wade Elliott struck Jay Tabb and dropped dangerously over the Reading crossbar.
It had come after a ten-minute spell during which Reading had looked particularly threatening, Reading were trying to maintain a quick, high-pressure tempo while Burnley wanted the opposite.
Full-back Dan Harding almost made the break through for the Royals when his free-kick skidded low through the defensive wall and Jensen was almost caught by surprise, clutching it at the second attempt.
At half-time Reading still had hope, but Burnley's second-half goals meant the Premier League dream was all over for the Berkshire club for another season, while the travelling supporters celebrated joyously.