Luongo got on the scoresheet in the 59th minute after a goal-mouth scramble following a corner.
The Socceroo started in midfield for the Owls.
Wednesday took the lead after 13 minutes through Connor Wickham.
Then Luongo made it 2-0 in the second half.
City pulled a goal back through a header in the 68th minute.
But the Owls held on to record the win.
The result sees Luongo’s side move to 13th on the Championship table, 10 points above the relegation zone and eight points from a playoffs place.