Paul Sturrock's Wednesday side had lost four of their last five away games, but Tudgay's first goals for 12 matches and Deon Burton's third since his arrival from Rotherham in January earned them a vital win.
Wolves, who forced their way back on to level terms in the 50th minute when half-time substitute Carl Cort scored his 11th goal of the season to cancel out Tudgay's opener, created a host of chances but were frustrated by on-loan Liverpool keeper Carson.
The highly-rated 20-year-old pulled off a string of stunning saves to leave Wolves' hopes of reaching the play-offs hanging by a thread.
Wednesday were fortunate to still be on level terms before Tudgay struck in the 44th minute.
Three times Carson pulled off wonder saves, starting after just 11 minutes when he held on to a free-kick from Lee Naylor.
The former Leeds United keeper then performed heroically twice just moments before Wednesday took the lead.
First, he turned away a deflected shot from Rohan Ricketts before preventing skipper Graham Coughlan scoring an own goal by scooping his mis-placed header from a Naylor centre around the post.
The full value of Carson's heroics became apparent when Burton strode down the left wing and whipped in a cross that Tudgay fired past Stefan Postma.
Wednesday's advantage would have been short lived if it had not once again been for Carson who pulled off another stunning save in first-half stoppage time to push away a header from Kenny Miller.
His resistance was finally broken five minutes into the second half after a spell of Wolves pressure when Cort rose high to head home a corner from Naylor.
Wolves were in the ascendancy after Cort struck but Carson frustrated them again in the 65th minute by denying Tomasz Frankowski.
It was to be a pivotal moment as Wednesday regained the lead two minutes later when Burton collected a long through pass from Chris Brunt and took the ball around Gabor Gyepes before firing a low drive past Postma.
Carson then produced two more vital saves to deny Paul Ince and Frankowski before Wolves' fate was sealed four minutes from time when another defensive howler from Gyepes allowed Tudgay to drill home his second goal from 15 yards.