A fifth defeat in six games left the Clarets in the Premier League’s bottom three as Crystal Palace eased their own concerns at the wrong end of the table.
Cardiff’s Friday night win over Wolves had pushed Burnley into the relegation places, with Palace only clear of the drop zone on goal difference.
But it was the Eagles who took off with a first win since mid-September as they ended their Selhurst Park goal drought.
Roy Hodgson’s side hadn’t scored from open play at home all season - and some of their finishing hinted at why.