The New Zealand striker emphatically converted from 12 yards to put Forest just 90 minutes away from a first European final in 46 years as they took a 1-0 first-leg lead.
But they will know there is still work to do if they want to try and follow in the footsteps of Brian Clough's side which won back-to-back European Cups in 1979 and 1980.
Vitor Pereira has some way to go before reaching Clough's status, but he has masterminded a stark turnaround of Forest's fortunes as they are now nine games unbeaten in all competitions.
Villa are by no means out of the tie even after a nine-game Europa League winning run came to an end at the City Ground, as nobody knows their way around a Europa League semi-final quite like Unai Emery.
A fifth title for the Spaniard is not out of his reach just yet, with Villa notoriously strong at Villa Park.
The decisive moment of the game came with 20 minutes left as Forest were awarded a penalty.
Morgan Gibbs-White's cross floated through to the far post and appeared to be out of play when Omari Hutchinson hooked it back into the outstretched arms of Villa defender Lucas Digne.
After a lengthy check Portuguese VAR Tiago Martins ruled the ball had not gone out and sent his compatriot Joao Pinheiro to the pitchside monitor.
The decision was a formality and Wood dispatched the spot-kick in commanding style, lashing past Emilio Martinez.
In the other semi-final, Freiburg goalkeeper Noah Atubolu saved a penalty but the Bundesliga team suffered a late 2-1 defeat to Braga.
Braga took an early lead through Demir Ege Tiknaz. Jordy Makengo cleared Rodrigo Zalazar's cross to the far post but the ball was recovered by Victor Gomez. He met Tiknaz, who slid the ball into the net with a touch in the eighth minute.
But the guests didn't take long to level. Jan-Niklas Beste crossed the ball to Vincenzo Grifo, who beat the goalkeeper to collect it and score in the 16th.
The hosts had a huge chance to retake the lead shortly before the break as they were awarded a penalty after Gustaf Lagerbielke was fouled inside the box by Philipp Lienhart. Atubolu, however, stretched out his arms to save Zalazar's spot-kick.
But the goalkeeper couldn't do anything to stop Mario Dorgeles's effort in added time as Braga held the advantage for the return leg in Germany next week.
Crystal Palace have one foot in the Conference League final after Ismaila Sarr scored the quickest goal in the competition's history to open their 3-1 semi-final victory over Shakhtar Donetsk.
The Senegal international scored 21 seconds into the contest at the Henryk Reyman Municipal Stadium in Krakow, where the hosts have played their home European games due to the ongoing war in Ukraine.
Oleh Ocheretko drew the sides level two minutes into the second half before Japanese midfielder Daichi Kamada became the Eagles' unlikely hero, firing them back in front two minutes before the hour.
He then turned provider for second-half substitute Jorgen Strand Larsen, who added a late cushion and fired Palace even further down the road to Leipzig with six minutes remaining.
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