The home side will take a single goal advantage into Tuesday evening's second leg thanks to a Graham Alexander penalty eight minutes from time.
Royals' boss Steve Coppell will no doubt wonder how his side lost this game after the visitors created by far the better openings but were thwarted by a man-of-the-match performance from Burnley goalkeeper Brian Jensen.
The visitors almost went in front midway through the first half when midfielder Jay Tabb was denied by a fine one-handed save from Jensen, who then held on to the rebound from Marek Matejovsky.
Jensen produced another parry 11 minutes from the interval but was indebted to striker Martin Paterson who cleared Kevin Doyle's follow-up attempt off the line.
The home side created few opportunities in the opening half with the Clarets only attempt at goal being pulled wide by Robbie Blake.
Both sides suffered injuries in the first half with Kevin McDonald replacing Joey Gudjonsson for Burnley and striker Dave Kitson replacing Kevin Doyle for Reading.
The second half continued in a similar vain with goalkeeper Marcus Hahnemann making a rare save from Paterson.
Whilst the respective midfields battled hard to create a semblance of a chance, both defences were generally well on top and so it seemed as if they would need an individual piece of brilliance or a mistake to break the deadlock.
In the end it was a mistake by central defender Michael Duberry, who pulled back substitute Steven Thompson and the ever reliable Alexander converted the spot-kick by sending the ball high to Hahnemann's left whilst the goalkeeper went the other way.
To complete a miserable few minutes, Andre Bikey was shown a straight red card by referee Martin Atkinson in stoppage time following a tangle with Blake.