After an end to end 67 minutes, United took the lead when a superb cross from Souleymane Doukara was powered home by a flicked header from Roofe to net his first goal for the Whites.
Villa rarely threatened thereafter and yet another Whites victory was assured in the fourth minute of injury time when Leeds countered through Hadi Sacko whose shot was saved by Pierluigi Gollini but trickled to Wood to smash the ball home from close range.
It took until the 12th minute for either side to create any sort of attempt on goal with Rudy Gestede's tame header from a Villa corner easily saved by Rob Green.
Leeds then wasted a 15th-minute free-kick awarded for a foul on Hadi Sacko which saw Mile Jedinak booked.
At the other end, Jonathan Kodjia then almost cashed in on hesitant Leeds play but Pontus Jansson and Kyle Bartley eventually swept up the danger.
From a misplaced Bartley header, Jonathan Kodjia was then an opportunity on the edge of the area but smashed a powerful effort wekk over the crossbar.
Villa then saw sclaims for a 21st minute penalty dismissed when Rob Green clattered into Albert Adomah but referee Peter Bankes waved away the appeals for a spot kick and replays show Green took the ball first.
Leeds hit back with Kemar Roofe hitting the side netting but United's best chance yet arrived on the half four mark when Pontus Jansson put a free header over the crossbar from Charlie Taylor's corner. The Swede held his head on the floor in frustration.
Leeds were gradually beginning to get going and the Whites were inches away from being awarded a 34th-minute penalty when Albert Adomah scythed down Charlie Taylor right on the edge of the box down the left hand flank.
Leeds wasted the free-kick and Pontus Jansson then saved Souleymane Doukara's blushes with a strong block to keep out a low shot from Gary Gardiner.
Back at the other end, Leeds then United squandered another free header inthe 39th minute through Kyle Bartle whose effort from Souleymane Doukara's cross flashed wide.
Kalvin Phillips was then booked for taking down Gestede and Villa again threatened when Gardiner's low effort was blocked by Bartley.
But Leeds squandered another potential opening in first half injury time when a wonderful pass from Kalvin Phillips picked out Sacko on the right wing but not for the first time a poor touch from the winger left the opportunity gone and the first half goalless.
Unlike in the first half, it took 13 seconds for a first attempt on goal in the second period with Kodjia lashing wide from 25 yards.
And after the intervention of a Leeds streaker, Villa squandered the game's best chance yet in the 53rd minute when Adomah powered through the centre of the pitch to advannce one on one with Green but flashed a low effort wide.
Within 60 seconds, Ashley Westwood's rising volley was parried away by Green as Villa began to up the ante.
But Leeds hit back with a spell of pressure of their own and Roofe saw claims for a 61st-minute penalty waved away when tumbling down in the area after a challenge from Jedinak.
At the other end, Green showed safe hands to gather a fierce long shot from Gardner who was then substituted for Jack Grealish.
All eyes were on the Leeds bench too to see if Whites head coach Garry Monk would make a change.
But he didn't need to as within two minutes of Grealish coming on, United took the lead through a fantastic header from Roofe.
From the left flank, Doukara delivered a beautiful cross into the Villa area and Roofe came storming through to beat keeper Collini to the ball and produce a glancing header into the corner of the net.
That gem of a cross proved Doukara's last act with Monk then bringing on Stuart Dallas with 17 minutes left.
After Jansson was booked for a pull on Westwood, Roofe then left the field to standing ovation in the 79th minute as he was replaced by Alex Mowatt.
Villa were having plenty of the ball but struggling to create a clear cut chance.
A woeful back pass from Jordan Amavi did little to help their cause in conceding an 88th-minute corner.
Villa were losing the plot and Jordan Ayew was booked after a scuffle between Grealish and Luke Ayling on the touchline.
Leeds had five minutes of injury time to survive but went close to adding a second when Wood smashed a close range effort at Gollini from Taylor's delivery.
But there was no denying Leeds their second goal in the fourth minute of injury time when Leeds countered through Sacko whose sheer pace carved out a one on one with Gollini.
Sacko's low shot was saved but the ball trickled to Wood to smash the ball home from close range in front of an ecstatic Kop.
Leeds United: Green, Ayling, Bartley, Jansson, Taylor, Phillips, Vieira, Sacko, Roofe (Mowatt 79), Doukara (Dallas 73), Wood. Subs not used: Silvestri, Denton, Berardi, Grimes, Antonsson.
Aston Villa: Gollini; Hutton, Elphick, Chester, Amavi; Westwood, Jedinak, Gardner (Grealish 67), Adomah (Ayew 76), Kodjia, Gestede (Abgonlahor 76). Subs not used: Sarkic, Cissokho, Bacuna, Tshibola.
Referee: Peter Bankes.