Albion knew an Elland Road victory would put them two points clear of Newcastle at the top and nine points clear of third-placed Huddersfield.
But home boss Garry Monk - who rolled the dice by leaving out lynchpin defender Pontus Jansson - got his game plan spot on and saw his men return to fourth.
The Whites were happy to play at a pedestrian pace for much of the first half but in Wood have the league's most lethal marksman, and he struck twice in the second half, once from the spot.
As a consequence, Huddersfield, Leeds and Reading will all feel one of the top-two berths can still be theirs as the season enters its final eight and, in Huddersfield's case, nine games.
There was a cagey start to the match representative of the stakes both were playing for, Leeds in particular content to keep the ball at the back.
It took 23 minutes for the first effort from either side, an off-target header from Leeds' Kyle Bartley, and that proved the spark the game needed.
Wood, the division's leading scorer, could not get his feet right as a loose ball fell near him in the box, while the striker was poised to nod in a Pablo Hernandez cross until Uwe Hunemeier cleared from under his own bar.
Brighton had barely been an attacking presence but would have been ahead 33 minutes in were it not for Leeds keeper Rob Green.
The veteran continued his fine recent form, palming away a goal-bound touch from his own player, Liam Cooper, off a Beram Kayal cross. Gaetano Berardi swept up the loose ball on the line.
Leeds - despite grievances over a Liam Rosenior tackle on Hadi Sacko - headed in relatively happy, but were given more to ponder as Brighton upped the ante after the restart.
It was the home side, though, to whom the game's first genuine opportunity fell on the hour.
When Lewis Dunk failed to clear a Berardi cross, Wood was the man Leeds would have wanted on it, 10 yards out and with only David Stockdale to beat. Slightly off-balance, his left-footed hit was comfortable for the keeper.
The Kiwi would have his moment 63 minutes in, though. Ronaldo Vieira won Leeds the ball with some tenacious play, Charlie Taylor stood up a fine cross and Wood looped a terrific header away from Stockdale and in.
Brighton naturally stepped up after the goal. Glenn Murray got free of Liam Cooper and hit wide and then found himself with space in the box, only for Green to brilliantly repel him.
But Wood had the final say, cracking in a penalty after Fikayo Tomori chopped down Souleymane Doukara.