Tudgay struck early on as Billy Davies' side extended their unbeaten home run to 34 league matches to move into second place.
Forest are now seven points behind leaders QPR with two games in hand and are in a good position for promotion to the Premier League.
Malky Mackay's visitors have now gone four games without a win in all competitions but remain in the hunt for a play-off push themselves.
Forest have made the City Ground a fortress under Davies and took just 51 seconds to open the scoring.
Paul Konchesky may have endured a nightmare few months at Liverpool but remains a class above most in the Championship and played his part in the goal.
The left-back carried the ball forward before playing it out wide to Chris Cohen. His low cross was gathered in by Rob Earnshaw who in turn teed up Tudgay who finished with aplomb with the outside of his right foot.
The visitors were understandably shell-shocked at the setback but had their first moment of promise in the 14th minute when striker Marvin Sordell lashed in a shot which Lee Camp turned aside.
Mackay's side were getting a foothold in the game and full-back Lloyd Doyley was next to test Camp's reflexes with a dipping effort which the goalkeeper did well to turn over the top.
Cohen then hit a snap shot at the other end which England Under-21 goalkeeper Scott Loach did well to parry before Earnshaw curled a free-kick wide as a bright first half came to an end.
Earnshaw flashed a shot across the face of goal at the start of the second half before Danny Graham had his first sight of goal.
The Hornets' top scorer had endured a quiet afternoon until the 50th minute when he wriggled free on the edge of the area to drill in a low shot which Camp gathered well.
The visitors forced a flurry of corners as they searched for a way through but Wes Morgan and Luke Chambers were in commanding form at the heart of the Forest back four.
Chambers almost nicked a second when he flicked a header wide from a Radoslaw Majewski corner before Forest substitute Nathan Tyson had the final effort of the afternoon when he shot straight at Loach from 20 yards.