The home side came close to breaking the deadlock in the 40th minute when Tresor Kandol's header was tipped over the bar by Hull goalkeeper Boaz Myhill.
Early in the second half Ryan France headed straight at Leeds keeper Tony Warner following a Sam Ricketts cross.
Leeds debutant Jonny Howson had a gilt-edged chance to score in the 75th minute but he scuffed his shot to leave Dennis Wise's team deep in trouble.
"Jonny Howson's only a baby, and it was a gamble, but he nearly got me the winner. He is a young lad with a lot of talent.
"He knows the game at an early age and in practice the other day he was the one who stuck out like a sore thumb.
"He's got good knowledge of the game and that's something that doesn't come too often."
Hull caretaker manager Phil Brown:
"The players dug in for me and showed exactly the type of character and commitment that we need.
"Hopefully I've bought the chairman more time with regards to appointing a new manager - and I don't think this will do my chances any harm."
Leeds: Warner, Richardson, Ehiogu, Heath, Lewis, Howson, Derry, Douglas, Westlake, Kandol, Blake (Healy 71).
Subs Not Used: Sullivan, Carole, Moore, Kilgallon.
Booked: Kandol, Howson.
Hull: Myhill, Ricketts, Turner, Delaney, Dawson, Marney, Coles, France, McPhee (Forster 28), Fagan, Bridges (Yeates 61).
Subs Not Used: Duke, Elliott, Byron.
Booked: France.
Att: 22,578
Ref: M Clattenburg (Co Durham).