After scoring a last minute penalty against Tottenham Hotspur in his first appearance for the club before the international break, Wood capitalised on a dreadful back-pass from Lee Chung-yong to give the Clarets the lead after just three minutes at Turf Moor.
Burnley spent most of the second-half on the back foot as Palace searched for an equaliser but the south east London side missed a litany of chances to haul themselves back into the game. Captain Scott Dann passed up the best of the opportunities, nodding wide from yards out with an open goal gaping. Christian Benteke was also denied by replacement goalkeeper Nick Pope after Tom Heaton was forced off with an injury.
Palace have now lost their opening four games of the season and are still to score a goal under De Boer, who insists he will continue to give "100 percent" to try and lift his side out of the mire.
A win for Sean Dyche's side lifts them up to seventh in the table.
The Magpies travelled to south Wales without manager Rafa Benitez as he continues to recover from a hernia operation but Lascelles' 76th minute header ensured a happy return to the north east. The Newcastle captain had an influential role to play at both ends of the pitch, making a crucial goal line block shortly before his goal to deny Tammy Abraham the game's opener.
Renato Sanches, whose loan arrival from Bayern Munich proved to be one of the most eye-catching deals of the final week of the transfer window, endured a disappointing debut and was replaced by Wilfried Bony after 69 minutes. Bony is back at Swansea for a second spell after leaving the club for Manchester City in 2015.
Newcastle meanwhile climb to 10th in the league.