After back-to-back defeats to Doncaster and Newcastle, Cardiff climbed up to fourth.
Meanwhile, Reading's worst-ever winless home streak stretches to 12 league matches since beating Wolves 1-0 on January 21.
It looked like it may not end that way after the hosts made a bright start. Cardiff keeper David Marshall was called upon inside the opening minute to push away Noel Hunt's shot from inside the box.
But that was as good as it got for Reading in the first half as their finishing failed to match their neat build-up play.
In contrast, Cardiff strikers Michael Chopra and Jay Bothroyd linked together well and caused all sorts of problems.
Reading keeper Adam Federici parried Bothroyd's shot after his strike partner had found him with a low cross after 18 minutes.
Grzegorz Rasiak should have done better than head wide on the half-hour mark following a pinpoint cross from overlapping full-back Shaun Cummings.
Cardiff looked dangerous on the counter-attack through Chopra and Bothroyd and the pair combined again just before the break.
Federici pushed away Chopra's shot from a tight angle before the Australian stood his ground to deny Bothroyd.
Reading emerged from half-time with renewed vigour and Brian Howard's 30-yard rocket forced Marshall into a fine save.
Less than a minute had elapsed before the Cardiff keeper had to tip another long-range effort from Marek Matejovsky round a post.
Marshall then denied Rasiak in the 55th minute before Hunt missed the target when he looked certain to score after being set up by the Pole.
So it was against the run of play when Burke blasted Cardiff into the lead soon afterwards.
Mark Kennedy and Peter Whittingham linked up well down the left side. Whittingham's cross evaded everyone in the box except Burke who took one touch to steady himself before driving the ball into the roof of the net.
The former Rangers midfielder should have put the game beyond Reading midway through the second half but, with the goal at his mercy, stood on the ball after Whittingham's cross found him unmarked at the far post.
Reading desperately chased the equaliser and Simon Church flashed a shot across goal and narrowly wide of the far post.
It looked like their cause might be aided by the 75th-minute dismissal of McPhail who was shown a straight red card by referee Paul Taylor for what he deemed to be a high challenge on Jem Karacan.
But Brendan Rodgers' side created little until injury time when Gylfi Sigurdsson volleyed straight at Marshall.
Then, from the Icelander's corner, Federici, who famously scored in injury time to earn Reading a 1-1 draw in this fixture last season, crashed an overhead kick goalwards.
But there was to be no repeat of those Boxing Day heroics as Marshall produced a superb save to deny his opposite number.