Karacan had come on in the second half after Jay Tabb was floored by a clearance by Burnley goalkeeper Lee Grant, which led to a lengthy delay.
The Royals had already had a penalty appeal turned down before Karacan stabbed home from fellow substitute Mathieu Manset's cross in the eighth minute of added time.
Both sides had chances to go ahead in the first half, with Charlie Austin just failing to get a crucial touch on Jay Rodriguez's shot before Reading striker Adam Le Fondre forced Lee Grant into a good save.
The visitors had a good chance to go in front after only five minutes when Joseph Mills' accurate corner found Kaspars Gorkss, but he headed over from close range.
Burnley began to find their rhythm and Rodriguez's snapshot took a deflection off Gorkss and just flew past the outstretched boot of Austin.
The home side began to dominate possession but they had Grant to thank for stopping them from going behind, when he made a good save from Le Fondre's shot after Andre Amougou's slip had let the former Rotherham striker in.
Moments later, Jay Tabb fired in a drive from 20 yards but Grant was always behind the strike and gathered well.
At the other end Kieran Trippier's deep cross was met by Austin, but his diving header failed to trouble Federici too much.
With half-time approaching a shot from Ross Wallace deflected off Jobi McAnuff, forcing Adam Federici to turn the ball over the bar. From the resulting corner, Wallace found Amougou but his header went high over the bar.
Reading suffered a blow when McAnuff was forced off at the break due to a knock and replaced by Noel Hunt.
With 55 minutes gone Marvin Bartley played a one-two with Austin and burst into the Reading box but his shot was well saved by Federici down at his near post.
That let-off seemed to wake the visitors up and an excellent delivery by Mills from a free-kick found Le Fondre, but he headed straight at Grant when he had time to control the ball before taking a shot.
Reading were forced into making a second change when Tabb caught a clearance from Grant square in the face and was strechered off in a neck brace and replaced by Karacan.
Referee Phil Gibbs incensed the visitors when he deemed Amougou's challenge on Le Fondre in the box to be fair.
However, they were celebrating at the death when Karacan connected with Manset's cross to give them all three points.