Vincent Kompany’s Clarets trailed to Tom Ince’s 56th minute finish when Yakou Meite flicked on goalkeeper Joe Lumley’s clearance.
The Premier League Hall of Famer made a double change just after the hour when Connor Roberts and Johann Berg Gudmundsson were replaced by Vitinho and Manuel Benson respectively.
The latter needed just five minutes to make his mark when drawing the home side level with his third goal of the season.
The former Royal Antwerp winger volleyed home from the edge of the penalty area after Royals’ captain Andy Yiadom had only partially cleared Josh Brownhill’s cross.
The visitors were denied a penalty deep into stoppage time when referee Jeremy Simpson failed to penalise Ian Maatsen’s trip on goal-scorer Ince.
And the away side’s misery was compounded moments later when Benson turned provider with a wonderful assist for Anass Zaroury’s last-gasp winner.
Here are the ratings from Turf Moor.
1. ARIJANET MURIC 7
Caught in two minds when Tom Ince raced onto Yakou Meite's flick on, but he couldn't do much to stop the first-time finish. Dealt with Reading's attempts to deliver the ball into the box, held on to Baba Rahman's rasping drive and was well-placed to collect Junior Hoilett's header. Photo: CameraSport - Rich Linley
2. CONNOR ROBERTS 6.5
Quelled the threat of Ovie Ejaria and Baba Rahman as Reading were starved of openings down their left hand side. Saw a first half header drift wide of the post from Anass Zaroury's cross and got forward well in support of Johann Berg Gudmundsson. Replaced by Vitinho just after the hour. Photo: CameraSport - Rich Linley
3. TAYLOR HARWOOD-BELLIS 7
The centre-back wasn't alert to Yakou Meite's flick on when Tom Ince raced goal-side to open the scoring. Withstood the physical and arduous challenge of Reading's former Ivory Coast international, getting tight to the forward to restrict his influence, and continued to impress with his quality on the ball when playing out from the back. Picked up an early booking. Photo: CameraSport - Rich Linley
4. JORDAN BEYER 7.5
Picked out as Burnley's man of the match after another almost unblemished display at the heart of defence. Faced a different threat when the visitors pushed with pace and power, but kept his composure, remained cool on the ball, and prevented Reading from making inroads in the final third. Recovered from a first half clash of heads with Baba Rahman. Photo: CameraSport - Rich Linley