Tudgay's second goal of an eventful game 18 minutes from time came after County had captain Ian Taylor sent off.
Derby took the lead in the 13th minute when Morten Bisgaard made the most of a misplaced pass by Brighton defender Kerry Mayo. The Danish midfielder exchanged passes with Grzegorz Rasiak before slotting home his first goal of the season.
Brighton were level within a minute, Mayo making amends with a cross which was headed in at the near post by Mark McCammon.
The visitors regained the lead on 43 minutes, courtesy of a blunder on his home debut by on-loan Blackburn keeper David Yelldell. The German-born giant blocked a hopeful cross from Jeff Kenna under pressure from Rasiak, and Tudgay toe-poked in the loose ball.
Brighton were back on terms again on the hour, as McCammon celebrated turning his loan move from Millwall into a permanent deal with his second goal of the game.
Michael Johnson's attempted clearance from a cross by Leon Knight rebounded in off the big centre forward.
Derby were at a numerical disadvantage two minutes later, the experienced Taylor seeing red for raising his hand to Knight.
County shrugged off Taylor's dismissal as Tudgay, born a few miles away at Worthing, lashed home a long ball from Kenna, which caught out the Brighton defence.
McCammon was twice denied his hat-trick by Derby keeper Lee Camp in a frantic finish, but County held on to chalk up their ninth away win of the season.