They have to be a little bit careful here, Burnley. There are undoubtedly three worse teams than them in this division but the gap remains slightly uncomfortable. Sean Dyche sits five points clear of the relegation zone. Crucially, five points clear of a besieged Cardiff City. Yet Burnley’s run-in is not a favourable one, Neil Warnock’s team the only one of the current bottom eight they face. How many points will Dyche actually pick up from now on, with Liverpool, Manchester City, Arsenal and Chelsea all to play? Crystal Palace took the lead after Burnley defender Phil Bardsley inadvertently turned the ball into his own net Burnley's Bardsley and James Tawkowski cut frustrated figures after the former's error gifted the visitors the lead Michy Batshuayi fired the visitors into a two-goal lead after providing a clinical finish from inside the box just after the break Wilfried Zaha skillfully cut in from the right to work it on to his left foot before unleashing a powerful low drive to score The Crystal Palace forward celebrated with his team-mates in front of the travelling supporters after sealing the victory Ashley Barnes flicked a header past goalkeeper Wayne Hennessey to score a late consolation goal for the home side MATCH FACTS, LIVE LEAGUE TABLE AND MATCH ZONE BURNLEY (4-4-2): Heaton 5; Bardsley 5, Tarkowski 5, Mee 5, Taylor 5; Hendrick 5 (Gudmundsson 46, 6), Cork 5, Westwood 6, McNeil 6 (Brady 72, 6); Wood 5 (Crouch 81), Barnes 6.5 SUBS NOT USED: Lowton, Gibson, Hart, Vydra SCORERS: Barnes (90) BOOKED: Mee CRYSTAL PALACE (4-3-3): Hennessey 6; Wan-Bissaka 7.5, Dann 7, Tomkins 7, Van Aanholt 8; Kouyate 8, Milivojevic 7.5, Meyer 6 (McArthur 71, 6); Zaha 8.5 (Townsend 79), Batshuayi 8 (Benteke 84), Schlupp 8 SUBS NOT USED: Ward, Ayew, Guaita, Kelly SCORERS: Bardsley OG (16), Batshuayi (48), Zaha (76) BOOKED: Milivojevic, Meyer REFEREE: Lee Probert 6 Premier League Premier League Championship League One League Two Scottish Premiership Scottish Div 1 Scottish Div 2 Scottish Div 3 Ligue 1 Serie A La Liga Bundesliga Michy Batshuayi made it 2-0 to Crystal Palace with a clinical finish from close range. CLICK HERE to see more from Sportsmail's brilliant MATCH ZONE feature. This chastening defeat against vibrant Crystal Palace is a significant worry for a team whose euphoric victory over Tottenham feels a lot longer ago than seven days. A worrying display at Newcastle and now this. Palace were electric when countering, their lightening front line frightening as they moved closer to securing safety for another year, opening up an eight-point lead on the bottom three. Despite not registering a shot on target and Wayne Hennessey’s flapping in goal, Palace went into the break ahead. That lead came after Phil Bardsley deflected past Tom Heaton, but Burnley should have thwarted the attack long before Jeff Schlupp’s 15th-minute cross. Burnley striker Barnes stretches at the back post and tries to toe poke the ball goalwards but can't direct it on target Crystal Palace goalkeeper Wayne Hennessey comes off his goaline and punches clear to relieve the danger Batshuayi wastes a glorious chance to score as Burnley goalkeeper Tom Heaton comes off his line to stop him in his tracks Burnley's Ashley Westwood and Crystal Palace's Wilfried Zaha (right) are kept apart by their team-mates Crystal Palace's Zaha gets brought down by a combination of Westwood and Jack Cork during the second half at Turf Moor Burnley manager Sean Dyche vents his frustrations on the touchline as he barks instructions to his players They gave the ball away in midfield and then failed to track the rampaging Cheikhou Kouyate, the Palace midfielder carrying possession 30 yards as markers merely mirrored his run. He found Wilfried Zaha, who had the comfortable beating of Charlie Taylor and then Schlupp struck onto Bardsley at the back post. Burnley missed chances. Chris Wood had the beat of them, only firing straight at Hennessey when sneaking in behind. Jeff Hendrick’s half-volley stopped by Patrick van Aanholt and Ashley Barnes could not sort his feet quickly enough when another opportunity arose. Two minutes after half-time and Palace did have a shot on target and did have their second. The coveted full back Aaron Wan-Bissaka’s enterprise saw him in the final third and the 21-year-old had the presence of mind to spot Michy Batshuayi, whose effort on the turn thumped beyond Heaton. By now Palace smelt blood on the break. Schlupp sauntered through the middle, unopposed again, and only a slight touch off James Tarkowski took it over the bar. Zaha was proving too good really, his feet too quick, his trickery winning countless free-kicks and agitating the natives. Dwight McNeil wraps his foot around a free-kick and manages to curl it over the wall but it doesn't trouble Wayne Hennessey Crystal Palace forward Zaha picks up the ball in his own half and looks to drive forward and set up an attack for the visitors Aaron Wan-Bissaka tracks back and times his challenge to perfection to dispossess Burnley forward McNeil Barnes volleyed wide after another awkward Hennessey punch, the goalkeeper still reacclimatising on a first Premier League start since January 12. For Burnley, it is the final ball. Or rather, the lack of it. Their most naturally gifted from wide areas, Johann Berg Gudmundsson, arrived at half-time for Hendrick, but they could not fashion enough space for the winger to hurt Hodgson’s back four. Batshuayi should have added a third when Bee Mee misjudged a routine long ball. Zaha eventually did it for him with 14 minutes remaining. Taylor and Mee was led a merry dance inside their own box, bamboozled by the feet again, and Zaha screeched an effort underneath Heaton. Barnes flicked past the hapless Hennessey to set up a tense finale. Substitute Peter Crouch forced a decent save from the goalkeeper as well but it was too late. Crystal Palace forward Batshuayi winces in pain after taking a knock in the midriff during the first half at Turf Moor Patrick van Aanholt tries to retain possession for his side as Burnley midfielder Jeff Hendrick applies some pressure Crystal Palace manager Roy Hodgson embraces his opposite number Dyche prior to kick-off at Turf Moor on Saturday All rights reserved for this news site dailymail and under his responsibility