Tudgay scored in the fifth minute and although Derby had their moments, substitute Leon Best scored the decisive second goal five minutes from the end in front of the 5,000 plus travelling supporters.
It was not the script that Derby had written after the new board of directors had been saluted by the fans before kick-off.
The local consortium, who took control of the club on Saturday, were given a standing ovation but that was as good as it got for Derby once referee Phil Dowd blew the whistle.
Wednesday were always the sharper team and they took an early lead when a low free-kick from the right touchline fell invitingly to Tudgay, who swept a low right-foot shot inside Lee Camp's left-hand post from ten yards.
Derby's best moment of the first half came when Morten Bisgaard whipped a 20-yard free-kick over the wall and Scott Carson made an excellent save diving to his left.
But Tudgay almost scored again in the 36th minute when he found space on the right-hand edge of the Derby penalty area, but Camp did well to keep out his low drive at the expense of a corner.
There were more problems for Derby when Paul Peschisolido was replaced at half-time by Lee Holmes, which meant that Bisgaard was pushed up front and there were few anxious moments for the Wednesday defence.
The closest Derby came to an equaliser was in the 74th minute when a cross from Marc Edworthy picked out Tommy Smith, but at full stretch he was unable to turn the ball past Carson.
Caretaker manager Terry Westley brought on Michael McIndoe in place of Bisgaard, but Derby's frontline lacked any real substance and Best wrapped it up with a breakaway goal in the 85th minute.
Tudgay, who had an excellent game on his return, played the ball up to the young striker, who held off Lewin Nyatanga before turning and hitting a right-foot shot which took a deflection off the Welsh defender before looping over Camp.
At the end, the Derby players emerged for the traditional end-of-season lap of honour, but it was the Wednesday supporters who had the most to celebrate as their team signed off on a winning note.