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.
But goals in either half from James McArthur and Andros Townsend were still enough to secure the most comfortable of wins which should have been more emphatic.
Joe Hart did his best to keep the Clarets afloat with a handful of fine saves.
But even his efforts weren’t enough to bring an end to a worrying run for Sean Dyche’s side, who must now re-group for back-to-back home games against Liverpool and Brighton before two more tough trips to London to play Arsenal and Tottenham before Christmas.
The Clarets had gone back to something like a tried and tested formula with Jeff Hendrick returning as the linkman between midfield and attack and Johann Berg Gudmundsson also back on the left flank following illness.
But the change didn’t inspire an immediate change of fortunes as Palace quickly grabbed control in pursuit of a first win in nine games.
Both of Palace’s two previous goals at home this season had come from the penalty spot. But it took them just 16 minutes to end the wait and go in front.
Hart had already made one superb save, touching away a low curling effort from Max Meyer at full stretch.
But the Clarets’ keeper was powerless to keep out an effort from McArthur, which was intended as a cross but eluded the touch of the on-rushing Meyer and squeezed inside the far post.
The busy Meyer was a constant threat and bent another shot inches wide as Palace looked to double the lead.
The Clarets at least steadied the ship and enjoyed a growing amount of possession.
But a half-chance for Chris Wood, who couldn’t reach a cross from Matt Lowton, was the nearest they came to an equaliser before half-time.
And it was Hart who was by far the busier of the two keepers and he did his best to keep Burnley in the contest.
The England international reacted well to touch over a deflected shot from dangerman Wilfried Zaha five minutes before the break.
And then following the re-start, he made an even better stop to deny the Palace talisman again as Zaha again made space to let fly.
The Clarets were hanging on by their finger-tips as Zaha then blazed over after being released by Townsend as Palace raided forward at will.
And captain Luka Milivojevic was then guilty of a worse miss when he dragged a shot wide of the target after a superb pass from Patrick van Aanholt had left him with a clear sight of goal.
When Hart denied Zaha again with an hour gone there was a feeling Palace may pay for their wastefulness, which increased further following Charlie Taylor’s remarkable block to keep out what looked like a certain second goal from McArthur.
But the Clarets couldn’t muster any pressure to spread doubt in the home ranks as it remained near one-way traffic with Zaha crashing a shot against the underside of the bar, Hart grabbing a header from McArthur as the Scotland international followed up.
Dyche had sent on Sam Vokes and the top scorer might have had a sniff of goal and an unlikely equaliser had he been able to control a fine ball forward from Taylor.
But with 13 minutes to go came the inevitable as Palace finally made it 2-0 to guarantee a first home win since the final day of last season.
And Townsend did it in style, again getting the chance to run at the Burnley defence and this time cutting in to arrow a delightful left-foot shot beyond a helpless Hart and into the top corner.
The visitors had barely created a chance and any prospect of giving Palace some late concern disappeared with five minutes remaining of a chastening afternoon.
Vokes' header down from only Burnley's second corner of the game was pounced on by Ashley Barnes, but the substitute lifted a close-range snap-shot over the top as the Clarets were given another stark reminder of the scale of the challenge now facing them.
Crystal Palace: Hennessey; Wan-Bissaka, Tomkins, Sakho, van Aanholt; Kouyate, McArthur, Milivojevic, Meyer (Puncheon 90); Townsend (Sorloth 88), Zaha. Substitutes: Guaita, Ward, Schlupp, Kelly, Ayew.
Burnley: Hart; Lowton, Long, Mee, Taylor; Gudmundsson, Cork, Defour (Vokes 60), Lennon (Brady HT); Hendrick, Wood (Barnes 79). Substitutes: Heaton, Tarkowski, Bardsley, Westwood.
Referee: Lee Probert