The Hornets opened the scoring when Clarke Carlisle pumped a long ball towards King, who turned and shot past Robert Green from a tight angle.
Young doubled the lead after 23 minutes, evading Adam Drury before beating Green from 25 yards.
King then hit the post before Ben Foster's parry fell for Kevin Lisbie to pull one back and Dean Ashton then struck the woodwork with a header.
Norwich boss Nigel Worthington:
"Two bad errors have cost us the game. You just shouldn't concede goals like that at this level.
"Having said that I can't fault the players for their effort and they had a lot of attempts on goal.
"We could easily have got something from the game but, as I said, we were guilty of some terrible defending in the first half and got punished."
Watford: Foster, Chambers, Mackay, Carlisle, Stewart, Devlin (Doyley 63), Blizzard (Bangura 63), Spring, McNamee (Bouazza 80), Young, King.
Subs Not Used: Chamberlain, DeMerit.
Goals: King 13, Young 25.
Norwich: Green, Colin (Doherty 81), Shackell (Davenport 45), Fleming, Drury, Marney, Safri, Hughes, Brennan (McVeigh 45), Ashton, Lisbie.
Subs Not Used: Jarrett, Gallacher.
Booked: Ashton, Lisbie.
Goals: Lisbie 62.
Ref: Paul Armstrong (Berkshire).