As things stand, Nigel Adkins's team occupy the final playoff spot on goal difference ahead of Blackburn Rovers.
The home side had their lead on 16 minutes when they broke from a Burnley corner and the counter-attack was eventually finished off by Kieran Trippier, who could only guide the ball into his own net as he tried to clear a cross.
However the Clarets were back in it moments later when Scott Arfield turned home his eighth strike of the campaign after Reading failed to clear a low cross.
Hope Akpan drilled a fierce effort into Shackell's legs after the visitors again failed to stop the ball coming in from a wide area, before Tom Heaton had to be alert moments later to deny a second own goal from Michael Duff.
Danny Ings gave his side the lead just before the half-hour mark when he netted his 26th goal of the campaign with a sharp turn and strike on the edge of the box.