The Clarets' record signing Chris Wood, captured from Leeds United for a reported fee of £15 million, scored after just three minutes of his first top-flight start to put the hosts in charge at Turf Moor, adding to his goal on debut against Tottenham before the international break.
Burnley proved unable to add to their tally but did enough to leave De Boer facing another week of heavy scrutiny should he survive inevitable calls for the club's hierarchy to make a change in the wake of a fourth successive defeat.
The arrival of former Ajax coach De Boer as Sam Allardyce's successor was intended to herald an elevation in the quality of the Eagles' playing style, but Palace are now the first top-flight team since the 1924-25 season to lose their first four matches without scoring a goal.
4 - Crystal Palace are the first top-flight team since Preston in 1924/25 to lose their opening four matches without scoring a goal. Flap.— OptaJoe (@OptaJoe) September 10, 2017
Indeed, Palace remain the only team across England's top four divisions who are yet to score this season, although Scott Dann missed a glaring opportunity to change that statistic in the closing stages, while De Boer's early tenure is ominously reminiscent of the poor start that saw him sacked by Inter in November last year.
The Dutchman must surely envy Burnley's strong opening to the campaign, which continued with a second victory from four matches, but manager Sean Dyche will anxiously wait to learn the extent of an injury suffered by goalkeeper Tom Heaton, the captain having been helped from the field in the 35th minute after hurting his left shoulder attempting to catch a high ball.
A sterner test may await the Clarets next weekend when they visit a Liverpool side reeling from a 5-0 thrashing at Manchester City on Saturday, while Palace's search for goals and points is set to continue at home to Southampton, although it remains to be seen if De Boer will still be in charge at Selhurst Park next weekend.
Burnley were gifted the lead after just three minutes when Lee Chung-yong, under pressure but in no real trouble near the half-way line, tried to find Wayne Hennessey.
The South Korea international badly misjudged the pass and left his goalkeeper stranded, Wood duly steering home an excellent first-time finish from outside the area.
2 - Chris Wood is just the second player from Oceania to score in their first PL start, after Brett Emerton for Blackburn in 2003. Kiwi.— OptaJoe (@OptaJoe) September 10, 2017
Palace had chances to offer a swift response, Dann seeing a shot cleared off the line by Matthew Lowton and Christian Benteke then heading wide under little pressure from the Burnley defence.
Having wasted those opportunities, the visitors almost fell further behind in the eighth minute, Sam Vokes nodding narrowly wide of the far post from Stephen Ward's delivery.
A lull followed that flurry of early activity, broken only by the worrying departure of Heaton, former Charlton player Nick Pope making his top-flight debut as the skipper's replacement.
The same pattern of play continued after the break, as Palace struggled in vain to create chances, Jeffrey Schlupp blazing a notable effort off target in the 71st minute.
Burnley, meanwhile, were content to frustrate the visitors and mount only an occasional threat on the break, Ashley Barnes calling Hennessey into action with a curling strike soon after Schlupp's wasteful attempt.
Pope made a good save to deny Benteke one-on-one with 11 minutes to go, while Dann had another goal-bound strike blocked by the heel of James Tarkowski.
Palace continued to probe for that elusive goal in the final minute and Dann unbelievably headed Yohan Cabaye's excellent cross wide from point-blank range to sum up the Eagles' malaise.
Key Opta stats:
- Crystal Palace are the first top-flight team since Preston North End in 1924-25 to lose their opening four matches without scoring a single goal.
- Palace have lost their last six Premier League games in which they have registered at least 60 per cent possession.
- Chris Wood is just the second player from Oceania to score in their first start in the Premier League – the other was Brett Emerton in August 2003 for Blackburn against Wolves.
- Wood's strike was scored just 169 seconds into the match, Burnley’s fastest Premier League goal since November 2016, also against Palace – Sam Vokes firing the Clarets ahead just 78 seconds in that match.
- Wood is the first Burnley player to score in both of his first two Premier League appearances for the club.
- Wood became just the sixth player from New Zealand to start a Premier League match, after Ryan Nelsen, Winston Reid, Simon Elliott, Danny Hay and Lee Norfolk.
- The Clarets are guaranteed to end today in the top eight of the top-flight outside the month of August for the first time since April 18th 1975.