Joe Mason's second goal in as many matches helped Cardiff reach a League Cup quarter-final for the first time since 1965. The 20-year-old broke the deadlock with a goal of rare quality, curling home a low, left-foot shot from just inside the penalty area.
The £250,000 signing from Plymouth Argyle, who scored his first goal for the club against Barnsley on Saturday, made an inauspicious start, firing wide of the Burnley goalkeeper Lee Grant's right-hand upright when clean through on goal.But the Republic of Ireland Under-21 international made amends shortly before the interval, drawing praise from the manager Malky Mackay
"I thought he was outstanding," Mackay said. "His intelligence on the ball and all-round ability and movement was there for us all to see. But I am sure that Joe will thank the midfield for giving him the chance to shine. They were excellent, too. The boy has great potential but we have to work hard to keep nurturing him. He has good people in terms of players and coaches around him and he's level-headed. If he keeps working hard he will only get better."
Mackay added: "We have to give due respect to the team we played. I was delighted with the way we passed the ball; we created three great chances in the first half and didn't allow them a shot in the second half."
Although both sides spent long periods of the match cancelling each other out Burnley had their chances, with Jay Rodriguez drawing a fine block from Mark Hudson and Keith Treacy and David Edgar forcing excellent saves from the Cardiff goalkeeper Tom Heaton.
Hudson should have scored a second for Cardiff after the interval and Mason had a goal disallowed for offside, but it proved to be immaterial as Burnley failed to capitalise on the lion's share of possession in the final 20 minutes.
The Burnley manager Eddie Howe said: "It was a positive start and on another day we could have scored a couple of goals. We also finished the game well and applied a lot of pressure with good possession, but we didn't work their keeper enough or hurt them in the second half."