Nigel Clough's side caused plenty of problems throughout and were only denied by the crossbar in the first half but the Brewers were finally unlocked seven minutes from time when substitute Doukara was fouled in the area and Wood smashed home his second penalty in a week for his tenth goal of the campaign.
Burton then had the chance to bag a dramatic leveler in the sixth minute of injury time through a free-kick right on the edge of the area but United scrambled the ball clear to release Doukara who eventually bundled the ball home in the 97th minute in front of a delighted and relieved Kop.
The result lifted Leeds up to ninth and just one point off the Championship’s play-offs.
Burton arrived at Elland Road having not won away from home so far this season but Clough’s side almost took the lead in the second minute.
A right flank corner met the head of Ben Turner whose effort was heading into the far corner and cleared off the line by Eunan O’Kane.
United’s first attack arrived through Kemar Roofe who raced away down the left wing but his low cross for Wood was cleared.
At the other end, Chris O’Grady bungled a delivery from Jamie Ward wide.
Two Leeds corners just before then ten minute marker then asked questions of Burton with a powerful Luke Ayling effort blocked by Jackson Irvine and hacked clear.
And United then created the game’s best chance so far after 14 minutes when Wood’s flicked header played in Pablo Hernandez who raced in on goal but he allowed ‘keeper Jon McLaughlin to smother the ball at his feet.
At the other end, Pontus Jansson made an important block to keep out a powerful effort from O’Grady before Leeds countered through Hadi Sacko who failed to play in Wood who was free on the opposite side.
And after a trademark sliding tackle from Jansson ended another Burton attack, United went mightily close to opening the scoring after 25 minutes when Sacko raced away down the right flank and sent in a low cross for Wood that was hacked behind for a corner by Ben Turner.
At the other end, Ayling had to make a crucial challenge to block a dangerous effort from Ward as Burton continued to threaten.
Ward then fired just wide minutes later with Leeds the next to threaten through Sacko who headed over from an angle after Charlie Taylor’s deep cross.
But after Sacko had flattened Lloyd Dyer to conceded a left flank free-kick, Burton were only denied the opening goal by the woodwork as Kyle Bartley’s back-header clipped the crossbar before going over for a corner with Rob Green completely beaten.
The Brewers were giving at least as good as they got with Leeds almost playing on the counter attack such as when a low effort from Kalvin Phillips was saved in the 40th minute.
Another Leeds break then ended with Sacko forcing Tuner to concede a corner which was cleared.
And United’s half was summed up in the sole minute of first half injury time when O’Kane was booked for hauling down Lucas Akins.
Burton boss Clough brought on Stuart Beavon for Ward during the half-time break and Beavon immediately went close after the restart, lashing a powerful volley just over the bar.
From a 50th-minute free kick on the left wing, Turner then squandered an even better chance when putting a free header over.
But Leeds finally threatened just before the hour mark when a lovely through ball from the impressive Ayling, who had been played through by Hernandez, fed Roofe whose low effort went inches wide of the left hand post.
United then began to turn the screw and another low effort from Roofe was gathered by McLaughlin five minutes after the hour.
Hernandez then twice went close with the Spaniard’s initial effort blocked and second attempt flying over the bar.
Burton hit back by forcing two corners and from the second of those headed just over.
Whites head coach Garry Monk then brought on Doukara for Roofe with 17 minutes left but Burton continued to cause bother and Jansson was booked for crunching Beavon just outside the box.
Matt Palmer drove the free-kick straight into the wall.
But an end to end game was finally unlocked in the 83rd minute when Hernandez played in Doukara with a sublime pass and the striker raced through the middle of the park and into the area before being upended by Turner in the box.
Referee Simpson sent the Kop wild by awarding a penalty - Turner booked in the process - and Wood made no mistake with his spot kick, smashing the ball home down the centre of the goal to send Elland Road mad.
Burton still refused to go away and two late corners caused panic before Monk brought on Ronaldo Vieira for Hernandez with one minute left.
From a Burton long throw, Naylor then blasted a fine opportunity straight at Green.
At the other end, Leeds had a chance to kill the game off but a low shot from Phillips was turned behind for a corner by McLaughlin after good work from Wood, who was probably better positioned for a shot himself.
Burton were then presented with their final chance when Vieira’s late challenge gave Burton a free-kick literally an inch outside the box.
Elland Road held its breath but Dyer’s effort hit the wall and the ball was eventually desperately scrambled clear, to such an effect that Leeds were able to counter and seal victory through Doukara in the seventh minute of injury time.
With Burton having practically played every player upfront, Wood fed Doukara with a slide-rule ball and the striker galloped his way through the middle of the field and in on goal before eventually scrambling the ball home at the second attempt after initially being hauled down.
Doukara was booked for celebrating as the striker booted the corner flag which went flying but the United attacker did not look remotely bothered.
All that mattered was that Leeds had won - again - with United now seven games unbeaten at Elland Road and now with 19 points from their last possible 27.
Play-off form certainly, with Leeds now just one point off the top six.
Leeds United: Green, Ayling, Bartley, Jansson, Taylor, O’Kane, Phillips, Sacko (Mowatt 90), Hernandez (Vieira 89), Roofe (Doukara 73), Wood. Subs not used: Silvestri, Cooper, Berardi, Antonsson.
Burton Albion: McLaughlin, McFadzean, Turner, Dyer, Palmer, Brayford, Irvine, Ward (Beavon 45), O’Grady, Williamson (Naylor 76), Akins. Subs not used: Mousinho, Bywater, Choudhury, Miller, Flanagan
Referee: Jeremy Simpson.
Read more at: http://www.yorkshireeveningpost.co.uk/sport/football/leeds-united/leeds-united-2-burton-albion-0-wood-and-doukara-fire-whites-to-periphery-of-play-offs-1-8208289