But Wood was not the only hero on the day as Burnley had to dig deep and ride their luck at times to keep a first clean sheet in the league this season and consign Palace to a fourth successive defeat without scoring a goal.
The club are said to have contemplated sacking De Boer during the global break, as the relationship between the manager and Palace chairman Steve Parish is reportedly "at breaking point".
"I will sign for this every game if we create that amount of chances against any opponent", De Boer said. "When I'm still the manager of Palace, I will give 100%".
With all of the top title contenders in action on Saturday and entertaining fans in some spectacular fixtures, the focus moved to a bottom-three side on Sunday, where Crystal Palace continued their horrendous start to the season.
Chris Wood's early goal for Burnley, which came courtesy of a horrendous error by Lee Chung-yong, turned up the pressure on De Boer, who has overseen the club's worst start to a season since 1925.
"It is not going to be an easy road, I am not guaranteed anything and it is going to come down to hard work and making sure I play well". It was clear that Palace needed to take their chances more efficiently if they wished to score.
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.
The Burnley boss was on Palace's shortlist following Sam Allardyce's shock resignation, but the south Londoners ultimately opted for De Boer as they looked to shift to a more possession-based approach.
"He has been active in the game and kept in touch with us throughout the game". "I am disappointed about the result but I am not disappointed about how we played".
There has been widespread speculation about the future of former Ajax Amsterdam coach De Boer, who arrived at Crystal Palace amid talk of transforming the team's style but who has yet to gather a point. De Boer himself shrugged off suggestions he had been given an ultimatum: win at Burnley or else. But the way I see it, it doesn't matter if they win or lose this weekend, at the end of the day this geezer is getting sacked - that is obvious to me and everyone.
De Boer's job is under threat but the Dutchman remains resolute, saying that his team's efforts in Lancashire give him "a lot of hope" for the future.