Sheffield Wednesday dented Cardiff's Championship play-off hopes by claiming all three points at Ninian Park.
Burton was given two bites at the cherry to score the Owls' second
Joe Ledley struck the Owls post, but Leon Clarke poked in Deon Burton's cross to give the visitors the lead.
Roger Johnson's header brought Cardiff level before the break, but Burton restored the lead after home 'keeper David Forde parried his first effort.
Cardiff's Simon Walton saw red on 90 minutes before Johnson's header was cleared off the line by Steve Watson.
Cardiff City boss Dave Jones:
"When you get your chances you have got to put them away at this stage of the season.
"We should've come away with something. They had two chances and scored.
"We are only three points off sixth place but it makes it more frustrating when the teams around you lose and you lose as well."
Sheffield Wednesday boss Brian Laws:
"It is highly unlikely but while it is mathematically possible we will have a go at it.
"Our away record is phenomenal and if we can match it at home you never know.
"Nobody has switched off and nobody is on holiday. At this stage, sometimes players tend to dip in form, but our players have stepped up their game."
Cardiff: Forde, McNaughton, Purse, Johnson, Ledley, Whittingham (Thompson 75), McPhail, Walton, Parry, Feeney (Green 82), Chopra.
Subs Not Used: Alexander, Flood, Gunter.
Sent Off: Walton (90).
Goals: Johnson 45.
Sheff Wed: Turner, Bullen, Watson, Wood, Gilbert, Tudgay, Whelan, Lunt (Folly 84), Brunt, Clarke (Lekaj 90), Burton (MacLean 86).
Subs Not Used: Adamson, Spurr.
Booked: Whelan, Wood, Burton.
Goals: Clarke 39, Burton 67.
Ref: M Russell (Hertfordshire).