Clarets boss Steve Cotterill named an unchanged team for the third consecutive game and they raced out of the blocks to take the lead as early as the fourth minute.
The goal came about when Cardiff were caught out by a quick throw-in taken by right-back Michael Duff.
The City defence failed to clear the ball and winger Steve Jones lashed a right-foot shot beyond goalkeeper David Forde from 20 yards.
The visitors' response came in the form of a series of corners, one of which, taken by Paul Parry from the right, was headed clear as far as Peter Whittingham but he volleyed over from 25 yards.
Goal-scorer Jones picked up a yellow card for a rash challenge on young full-back Chris Gunter but Jones then turned provider by rounding Gunter and crossing for Andy Gray to send a header against the crossbar with Forde well-beaten.
Cardiff enjoyed more of the possession in the first half and, from another Parry corner, central defender Roger Johnson was unlucky to see his effort cleared off the line by James O'Connor.
Burnley striker Andy Gray incurred the wrath of referee Beeby and received a yellow card in first-half stoppage time for persistent fouling.
The home side extended their lead just three minutes into the second half as Jon Harley found Gray, he swept the ball wide to Wade Elliott whose near-post cross was volleyed past Forde by on-loan striker Paul McVeigh.
McVeigh almost immediately got on the score-sheet again but this time was denied by Forde at the expense of a corner.
Left-back Harley became the third Claret to receive a yellow card while Cardiff boss David Jones introduced all three substitutes in an attempt to get something out of the match.
Central defender Wayne Thomas and winger Elliott also picked up yellow cards much to the displeasure of the home fans.
Cardiff's miserable afternoon was completed when youngster Gunter headed the ball past home keeper Brian Jensen only to see his effort disallowed for offside.
The result gave Burnley a third successive victory and banished any prospects of relegation.