Malky Mackay's Carling Cup runners-up headed into the game on a run of two wins in nine league games that left them looking up at the top six.
Burnley - now 10 points shy of the play-off places with as many games to play - welcomed boss Eddie Howe back to the touchline following the death of his mother and made most of the running in the first half, only to find Bluebirds goalkeeper David Marshall in inspired form.
The home faithful made their dissatisfaction with their side's efforts clear at the break and the Bluebirds displayed renewed intent after the break, although Lee Grant did not have a save of note to make in the Burnley goal.
Cardiff lie a point behind sixth-placed Middlesbrough, who have a game in hand.
Mackay kept faith with the line-up that lost 3-0 to Hull in midweek, although Stephen McPhail was named among the substitutes after Filip Kiss pulled out through illness.
Burnley's top scorer Jay Rodriguez lost his ever-present appearance record this term due to a groin problem, while hamstring injury victim Junior Stanislas made his first start for two months and Danny Lafferty earned a Clarets debut at left-back.
Ross Wallace was at the heart of an enterprising start from Burnley as Martin Paterson's shot from his cross was deflected behind, before Marshall found himself at full-stretch to tip a 25-yard drive behind from the Scottish winger.
The hosts responded in the 12th minute when Joe Mason rounded Grant, but he was forced wide and the chance went begging.
Burnley remained in the ascendancy as Danny Ings sent a sweetly-hit volley narrowly over and David Edgar headed Kieran Trippier's free-kick past the upright, while Paterson and Stanislas drew further fine stops from Marshall.
In the 36th minute Ings cut in from the left flank to fizz a shot just wide. Cardiff held out until the interval but it did not stop them being booed from the field by sections of the home support.
The visitors looked to retain their momentum in the second half, but opportunities had dried up by the time Stanislas thumped a 25-yard free-kick over with an hour gone.
Cardiff were showing renewed intent, epitomised by the tireless work of Liam Lawrence on the right side of midfield, and Aron Gunnarsson was inches away from heading home an inviting cross from the former Stoke player.
Mackay's men finally assumed the upper hand as the game entered its final quarter, with Burnley striker Ings back to hack clear under pressure in his own penalty area before Bluebirds full-back Andrew Taylor drilled wide from the edge of the box.
Robert Earnshaw came off the bench and almost earned Cardiff the points with a deft glancing header, while fellow substitute Charlie Austin shot wide under pressure at the other deep into stoppage time as the deadlock remained intact.