Sean Dyche's Clarets had slipped into the relegation zone ahead of kick-off following Cardiff's dramatic 2-1 victory over Southampton, but they responded in style as composed finishes from Wood either side of half-time put them in control at a rain-soaked Amex Stadium.
The visitors, who were also indebted to an inspired first-half display from goalkeeper Tom Heaton, went further ahead through Ashley Barnes' penalty, before Shane Duffy pulled one back for the Seagulls.
Success on the south coast stretched Burnley's unbeaten run to seven top-flight games, leaving them level on 27 points with their out-of-form hosts.
Albion have been sucked back into relegation danger after taking just two points from a possible 18 during a six-game winless streak since the turn of the year.
Brighton defender Gaetan Bong was once again subjected to boos from opposition fans in reference to last season's racism row with Burnley-born West Brom striker Jay Rodriguez.
Cameroon international Bong, who accused former Clarets player Rodriguez of making a racist comment during a match in January 2018, was also jeered at Turf Moor last April and during the midweek FA Cup win against the Baggies.
In contrast, the home supporters had plenty to cheer inside the opening five minutes.
A powerful Solly March header from a Bong cross had to be tipped over by Heaton, before the keeper produced an even more impressive stop to keep out Pascal Gross' powerful volley.
Only a handful of Burnley fans made the long trip south for the televised evening kick-off and they should have been celebrating the opening goal in the 17th minute.
Dwight McNeil's initial cross from the left was diverted on to the crossbar by Albion defender Duffy, before Barnes headed the rebound against the woodwork with the goal gaping.
After Heaton again saved from March, the visitors made the most of their next opportunity to edge ahead.
An untimely slip from Brighton captain Dunk allowed Wood to race on to Barnes' hopeful ball forward and emphatically bury the ball past Ryan.
There had been just one goal in the previous three Premier League encounters between the clubs but this was proving to be a far more open affair.
Heaton's fingertips on a Gross cross denied Glenn Murray a simple headed finish, while Clarets midfielder Jeff Henrick cleared Duffy's thumping header off the line from a Gross corner.
Winger March was arguably Albion's best player in the first half but he was substituted early in the second period due to an apparent injury.
Without him, the Seagulls struggled to create and they fell further behind in the 61st minute.
Teenager McNeil produced a marauding run forward before slipping the ball to his left for Wood to calmly slot into the bottom right corner via the hand of Ryan.
The Clarets then wrapped up the points in the 74th minute following an action-packed sequence.
After Hendrick escaped penalty appeals for a possible handball, Barnes broke clear at the other end and was brought down by Ryan before Wood, searching for a hat-trick, slotted wide of the empty net.
Referee Stuart Attwell brought play back to award the penalty, allowing Barnes, another ex-Brighton player, to stroke the ball into the bottom left corner for his second successful spot-kick in as many games.
Any hopes of the visitors seeing the game out without incident were dashed just two minutes later though as Duffy rose to head home his fifth league goal of the campaign from Anthony Knockaert's searching free-kick, but Brighton were unable to fight back.