Palace started the game without Wilfried Zaha as he was self-isolating at home, so Michy Batshuayi came in to replace the Ivorian forward. The game went sour for Palace quickly as Wood capitalised on a Cheikhou Kouyate error to give Burnley an early lead.
Story of the Match
The Eagles started well when Nathaniel Clyne hit a shot from distance to test Nick Pope early on, but it was Wood who gave Burnley the advantage after just eight minutes - courtesy of Kouyate's poorly timed header, which allowed the New Zealand international to smash home.
Wood's goal ended a run of 324 minutes of Premier League football without a goal at home for Burnley.
Burnley gained confidence and Jay Rodriguez was causing trouble, especially against Kouyate, who was struggling to deal with Rodriguez and Wood all evening.
Palace came close shortly after when Eberechi Eze went on a mazy run to put through James McArthur - the midfielder squared the ball to Batshuayi, who came agonisingly close to getting his foot on the ball.
The Eagles were getting back into the game and Batshuayi came close again when he ran from the middle of the pitch and hit his effort just wide of the far post.
Chances were coming for Palace as Andros Townsend tested the palms of Pope from distance, after cutting inside on his left foot.
Shortly after the interval, Johann Berg Gudmundsson had a great chance to double the lead for the hosts but his effort hit the bar following a great pass from Dwight McNeil.
Moments later, a Burnley error allowed Batshuayi through on goal but he could only shoot straight at Pope, and a glorious chance for the equaliser was wasted.
Wood had the chance to get his double. Another Palace error allowed the striker a clear opportunity against Vicente Guaita, however, standing tall, the Spaniard denied Wood this time round.
Substitute Christian Benteke had a golden chance near the end of the game to equalise for Palace, but Pope excellently saved to deny the Belgian. Palace's late pressure couldn't break the Clarets' resolute defence, as the hosts held out for an all-important win.
Nightmare performance from Kouyate
The Senegal international was abysmal this evening and he looked shaky from the start, with his woeful header gifting Wood an easy chance to convert.
Scott Dann had to cover for Kouyate all game, especially he was out-of-position and not getting goal side of Wood or Rodriguez, whenever Burnley played a ball over the top.
Wood bullied Kouyate and it looked like he'd never played at centre-back before. The man was a shadow of the player we've seen all season and he will need to improve on Friday night if Palace are to get anything against Newcastle United.
Zaha's absence caused a struggle in creativity
Since the start of the 2014/15 season (when Zaha re-joined Palace), the Eagles have lost 20 of their last 28 Premier League games without the starman (W7 D1).
This statistic included each of the last seven away from home which proves that Zaha is simply irreplaceable and Palace must do everything in their power to stop him leaving.
Eze offered an alternative, but no one was on his wavelength and the England under-21 international struggled to link-up with Batshuayi and Jordan Ayew.
Burnley's defence and Wood's goal was the difference
The Clarets got their first clean sheet of the season and they worked incredibly hard to get it.
The partnership of Ben Mee and James Tarkowski was key to stopping the advances of Eze and Batshuayi, who threatened the pair on many occasions.
Wood's goal may have been an easy chance but his awareness to pounce on an error quicker than everybody else - proving that his poor recent form is just a blip. The Kiwi international is back and he will prove to be crucial for Sean Dyche's men.
The Eagles play against Newcastle on Friday night live on Amazon Prime Video at Selhurst Park whilst the Clarets face a tough away game against Manchester City on Saturday afternoon.