It ended a run of two successive defeats for the Welsh side, but means that the Royals have failed to win at home in the league since January 27.
Reading's problem is clear. They play a neat passing game, but lack penetration up front and Brendan Rodgers has a real problem on his hands with his side's lack of firepower.
A goalless first half left supporters wondering where a Reading goal would come from and it seemed their fourth 0-0 draw in seven league matches was a strong possibility.
Busy midfielder Brian Howard raised hopes briefly after the re-start with a shot that David Marshall turned round his post for a corner and then Marshall saved from Marek Matejovsky as Reading increased the pressure.
Next to try for Reading was Irish international striker Noel Hunt but from six yards out he failed to connect with Grzegorz Rasiak's pass.
Marshall was in action again with a comfortable save from Rasiak as Reading played their best football of the game.
Cardiff were still hopeful of grabbing a goal in a breakaway and it came just after Reading had made a substitution.
Rodgers replaced Hunt with Welsh international striker Simon Church, but it was Cardiff who grabbed the vital goal.
Peter Whittingham, making his 100th league appearance for the Welsh side, sent over a cross from the left wing and from close range Burke hammered a shot high into the Reading net.
Cardiff's joy was spoiled by a red card for Stephen McPhail near the end after a tackle on Jem Karacan.
Last season Reading snatched a last-minute draw against Cardiff with an equaliser from their Australian goalkeeper Adam Federici.
The Royals tried the trick again as the game went into five minutes of added time. Federici went up for a corner, tried a spectacular overhead kick, but it was comfortably saved by Marshall.