When all looked headed for a stalemate, the winger, a 71st-minute substitute, scored in extra-time to give The Lions a 2-1 lead, before Tammy Abraham added another goal two minutes later to seal three points away at Hillsborough Stadium.
The strike is the Black Star's third in 30 league matches involving 17 starts this season.
The win has sent Villa to fifth on the league table while Sheffield Wednesday occupy the 12th position.
Interestingly, it was the home side who scored the opener through Gary Hooper in the seventh minute.
John McGinn, however, levelled the score with a 22nd minute strike, which lasted until the second minute of injury time when Adomah pounced on a rebound to make it 2-1 after goalkeeper Kieren Westwood parried Jonathan Kodjia's effort.
Then, Abraham killed the game in the 94th minute, squeezing the ball under Westwood into the back of the net.