The Royals were crushingly denied a place in the play-offs by an injury time goal at the City Ground, earning Brighton the win that they needed to pip Reading to sixth spot by a point.
A heartbreaking end to the season for Reading, who had played well against already promoted Burnley and earned a point that looked like it might be enough.
Reading had taken the lead through a Kieran Trippier own goal, but the Clarets had bounced back with two goals in eight minutes from Scott Arfield and Danny Ings.
Garath McCleary's second half wonder goal drew Reading level and it seemed as though the Royals would earn sixth spot until Brighton stole all three points at the death and Reading had no time to react.
Subs: Federici, Cummings, Gorkss, Hector, Blackman.
Burnley: Heaton, Trippier, Mee, Duff, Shackell (c), Jones, Marney, Arfield (Stanislas 72), Kightly (Wallace 63), Barnes, Ings.
Subs: Cisak, Edgar, Long, Treacy, Baird.
Yellow: Arfield, Mee, Duff.
Referee: Mr M Russell
Attendance: 23, 335 (2,021 away)
Within the opening minute, Reading were surrounding the referee appealing for what seemed to be a certain handball by Jason Shackell. The Burnley skipper blocked Pavel Pogrebnyak's right-footed shot with his arms and the referee awarded nothing, pointing for a goal kick after Garath McCleary had fired over moments after the incident.
The Royals had come out of the traps fast and Jobi McAnuff's low cross from the left almost found its way to McCleary at the far post only for Mee to hack the ball clear.
And on the quarter hour mark, Nigel Adkins' men got their reward for a lightning fast start. Obita lashed clear from inside our own box and Mikele Leigertwood nodded it powerfully away again from the edge of the box, finding Le Fondre in the centre circle. Alfie acted fast to hook it into space and McAnuff burst onto it down the right. He crossed low into the area looking for Chris Gunter and Kieran Trippier slid in to turn it past his own keeper and send Madesjki Stadium wild.
But the joy was short-lived. A cross from the right wasn't cleared and the ball fell scrappily to Scott Arfield, who arrowed it high into the Royals goal to level matters very much against the run of play.
Reading almost regained the lead moments later when McCleary did quite brilliantly to beat two men down the right and cross into the box. The ball was only scuffed out to Hope Akpan who hooked a powerful effort on target, but it cannoned into a Burnley body and behind for a corner.
At the City Ground, Nottingham Forest took the lead against Brighton, while Blackburn led Wigan 2-1, but back at Madejski McAnuff almost carved out a second own goal with a cross from the byline on the left this time, the low centre ricocheting off Michael Duff and into the unknowing Tom Heaton at the near post.
But with their second shot at goal, Burnley scored again, Danny Ings swivelling on the edge of the area and arrowing just wide of McCarthy's dive and inside the bottom left corner.
McCleary looked to respond immediately, driving from distance with his right foot but Heaton well behind it in the Burnley goal.
But with the second goal, the Clarets had dampened the atmosphere a little and Burnley were beginning to command possession, Ings almost scrapping an effort towards goal from yards out as half time began to draw near.
On the stroke of the interval, McAnuff delivered a corner into the box which Morrison met, but the centre half couldn't get enough power to his header to trouble Heaton.
But before half-time could arrive, Alex McCarthy produced a wonderful save to deny Ings who was through one on one with the keeper following a ball from the back that looped over the top of the Royals back line. Morrison got enough on the rebound effort the deflect it behind for a corner and Reading survived a scare.
Brighton then levelled at Forest, meaning the Royals dropped out of the top six with little more than 35 minutes of the season remaining - Nigel Adkins introduced Jake Taylor for Hope Akpan shortly after, and then Le Fondre had to withdraw with an injury, Hal Robson-Kanu coming on.
And from nowhere, Reading levelled...in incredible style! A long free kick from Morrison was only headed as far as Garath McCleary who got underneath the dropping ball and volleyed into the top left corner to score arguably one of the finest goals ever seen at Madejski Stadium. Reading had edged back into the play-off places...for now.
Burnley quickly regained their composure and McCarthy did well to save from David Jones, palming his drive from distance away and Gunter hacking it further up field.
Pogrebnyak then flew down the left wing before cutting the ball back to Hal Robson-Kanu in the area and the Royals winger controlled and turned and shot, but it was well charged down by a Burnley body.
With 20 minutes remaining, Gunter won a free kick on the right that Obita delivered deep to Pearce at the far post. He headed it back into the six yard box and a scrap ensued, but no-one could turn the ball home in a crowded box.
Taylor tried his luck from distance but it was easy for Heaton to gather on his line.
Then it seemed as though Reading would score a third, McCleary cutting the ball back to Pogrebnyak, who did well to get it out from under his feet to place a left-footed effort past Heaton only for Shackell to clear off the line with a last ditch slide.
Then another glorious chance presented itself, Robson-Kanu threading a delightful ball into the feet of McCleary, but one on one with Heaton the Clarets' stopper got a foot to his low shot to save. Were the gods against us?
With seven minutes left on the clock, Alex Pearce directed a header towards goal, but Heaton leapt to his left to save quite comfortably. A goal conceded and Reading would drop out of the top six, a goal scored and Brighton's result would become irrelevant.
Stanislas forced a save from McCarthy and the Royals keeper clung on to the shot well, then Robson-Kanu crossed from the right flank but McCleary could only head wide at the far post.
Three minutes of injury time were signalled and five at the City Ground, in which Brighton dramatically took the lead. A Jordan Obita corner kick was headed goalwards and Heaton flapped it off the line - Reading needed to score all of a sudden!
But there was no time. It was all over at Madejski Stadium and Brighton held on to the lead they stole in injury time to take them into the top six in the final seconds of the season.