A first-half goal from Bakary Sako was enough to continue Crystal Palace’s revival under Roy Hodgson as the Clarets’ winless Premier League run extended to six games.
Three of those have been draws and only once in that sequence has Sean Dyche’s men lost by more than a single goal.
And that was the fine margin that separated the sides at Selhurst Park as Burnley’s three-match unbeaten run away from home was ended by a Palace side which has seemingly banished its relegation fears under the former England boss.
Hodgson was appointed after Frank De Boer’s five-match reign was ended after a 1-0 defeat at Turf Moor in September left Palace without a point or a goal.
They have now amassed six wins but the latest one didn’t come without a struggle as Burnley recovered from a poor first 45 minutes to push Palace all the way and go close to taking a point in a frantic finish.
While the Clarets brought back three players following their FA Cup exit to Manchester City – meaning starts for Phil Bardsley, James Tarkowski and Steven Defour – Palace made four changes after they went out of the competition to Brighton.
However, Sako kept his place after scoring in that game and the former Wolves frontman fully justified his first league start since September.
He was a constant threat to the Clarets with his pace and power, forcing Tarkowski into an early challenge which saw the defender – whose first Premier League start had come on this ground in April in a first away win of the season which all but secured top-flight safety –get just enough of the ball to get the verdict from referee Michael Oliver as Palace appealed for a penalty.
But next time Sako got into the box there was to be no reprieve for the Clarets as he put the Eagles in front with his sixth goal of the season with 20 minutes gone.
Allowed to run too far into the danger area, his low shot skidded past two pairs of legs, unsighting Nick Pope, who was unable to keep the ball out of the net with his left foot.
Palace, beaten just once in 11 league games, looked to capitalise with a intense spell of pressure for the next five minutes which had Burnley on the ropes.
Only a superb goalline clearance from Ben Mee denied James McArthur a second goal as he raced into tap home Wilfried Zaha’s lofted ball over Pope, who had been sold short by Charlie Taylor’s attempted headed back-pass.
Sako then had an effort blocked at the near post by Tarkowski, with Christian Benteke heading the resulting corner just over the top.
And then after the Clarets had briefly stemmed the tie and gone close for the first time through a Sam Vokes header and an Ashley Barnes shot tipped over the bar by Wayne Hennessey during their best spell of the half, Sako was only inches away from making it 2-0 at the break with a thumping volley which flew just wide from Timothy Fosu-Mensah’s cross.
The same combination brought Sako another heading chance on the break early in the second half but the Clarets knew they were still in the game and threatened to wipe out Palace’s lead when Barnes nodded a Johann Berg Gudmundsson cross just wide and Vokes flashed a header into the side-netting from Defour’s delivery at the end of an excellent counter-attack.
A vital block from Taylor – who came through a major test with credit – on Zaha at the other end preserved the status quo and with 25 minutes to go Dyche sent on Georges-Kevin Nkoudou for his debut on the left flank and made the switch to 4-4-2.
The on-loan Tottenham man made a positive start as Palace’s grip was loosened and the Clarets stepped up the pressure in search of an equaliser.
Nkoudou’s ability to run with the ball helped push Palace back as the tension built around Selhurst Park with a second successive win within touching distance.
And the chance for Burnley to deny them it came with seven minutes to go, Defour lifting the ball over the top for Barnes to slide in and connect with an effort which Hennessey was able to smother as he raced off his line to meet the Clarets’ striker head-on.
The Clarets kept plugging away and bombarded the Palace penalty area in stoppage-time but the home side held out, thwarting the attempted comeback but still leaving Burnley seventh in the table - three points clear of Leicester City in eighth.
Burnley: Pope, Bardsley, Tarkowski, Mee, Taylor, Gudmundsson (Wells 86), Defour, Cork, Barnes, Hendrick (Nkoudou 64), Vokes. Substitutes: Lindegaard, Lowton, Westwood, Walters, Long.
Booked: Defour, Bardsley, Taylor
Crystal Palace: Hennessey, Fosu-Mensah, Tomkins, Kelly, van Aanholt, Milivojevic, Riedewald, Sako, McArthur, Zaha, Benteke. Substitutes: Speroni, Cabaye, Lee Chung-yong, Souare, Kaikai, Delaney, Wan-Bissaka.
Referee: Michael Oliver