He reacted quickly inside the area when Frazer Richardson's cross dropped at his feet, turning to fire into the roof of the net from six yards.
Hulse had earlier hit the woodwork with a header from an Eddie Lewis corner but Norwich had chances of their own.
Leon McKenzie and Dean Ashton both failed to hit the target and Darren Huckerby blazed wide for the Canaries.
Leeds manager Kevin Blackwell: "It's how we do over a season that counts, not four or five games.
"The results we have picked up so far have given us a platform, a start, and
that's all. Now we've got to go out and build on that.
"This club is big enough to go up, there's no doubt about that, but I'm not going to say we will go up. There is an awfully long way to go yet."
Norwich: Green, Colin (Doherty 79), Fleming, Shackell, Brennan, Marney, Safri, Charlton (McVeigh 87), Huckerby, McKenzie, Ashton.
Subs Not Used: Ward, Jarrett, Henderson.
Leeds: Bennett, Kelly, Butler, Gregan, Harding, Richardson, Einarsson, Derry, Lewis, Healy (Cresswell 74), Hulse (Douglas 79).
Subs Not Used: Sullivan, Kilgallon, Blake.
Booked: Hulse, Lewis.
Goals: Hulse 67.
Ref: U Rennie (S Yorkshire).