New Zealand international Wood marked his maiden appearance for Burnley at Turf Moor following his club record £15 million ($19 million, 16 million euros) move by firing the winner early in the first half.
The former Leeds striker punished a woeful backpass by Palace’s South Korean winger Lee Chung-Yong.
For Palace manager De Boer, his side’s fourth successive defeat could bring an abrupt end to his first season at Selhurst Park.
Palace have yet to score a league goal since Ajax and Inter Milan coach De Boer took charge and reports ahead of this fixture claimed Eagles chairman Steve Parish was already considering sacking the Dutchman.
With Parish watching from the stands, De Boer saw second bottom Palace waste a string of chances to at least snatch a point and he will head back to south London with his future in doubt.
“I am just focusing on what I can control and so are my staff and my players,” De Boer said.
“The future is for other people to decide but while I’m the manager of Crystal Palace I will give 100 per cent.
“We have to look in the mirror and be responsible that you have to take the chances, and you get punished when you don’t.
“But if you look all over at how we showed spirit, I think we were quite dynamic. What we showed today gives us a lot of hope for the future.”
Desperate to spark Palace into life, De Boer had made three changes and reluctantly switched to a 4-4-2 formation in a bid to kick-start his season.
But it took just three minutes for his plans to go horribly wrong.
Lee, making his 100th Premier League appearance, turned and played the ball back in the direction of the non-existent Palace defence.
Wood reacted superbly, intercepting the pass and slotting past Palace goalkeeper Wayne Hennessey first time from the edge of the area.
Palace were almost level within a minute when Scott Dann took aim from the right side of the box and his deflected shot was booted off the line by Matthew Lowton.
Two minutes later Palace came close again when Andros Townsend lofted a pass to Christian Benteke, who steered his header inches wide of the far post with keeper Tom Heaton beaten.
Burnley suffered a setback just past the half-hour mark when Heaton was forced off with a shoulder injury after landing awkwardly, giving a Premier League debut for 25-year-old Nick Pope.
Jeffrey Schlupp blazed over as Palace applied late pressure.
But Benteke was denied by Pope in the 78th minute, then Dann headed wide from no more than four yards out to ensure another dismal afternoon for De Boer.
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