Both the Foxes and the Whites had opened their campaigns with back-to-back 2-1 victories in league and cup, but neither could find a way through in their meeting at the King Power Stadium.
The hosts came closest, with substitute Chris Wood hitting the woodwork in the 82nd minute.
Leeds skipper Rudy Austin impressed in central midfield on his return from injury as the visitors held out for a point.
Jason Pearce had the best chance of a forgettable first half, but failed to get his fifth-minute header from a Noel Hunt right-wing cross on target.
Pearce and Zak Whitbread both collected yellow cards in the opening period as Brian McDermott's tactics frustrated the hosts.
After the break, Nigel Pearson threw on Lloyd Dyer and Anthony Knockaert in a bid to spark Leicester into life.
Jamie Vardy saw a header deflected over, before a clear sight of goal finally arrived in the 66th minute. Danny Drinkwater was the recipient of it, taking in Liam Moore's pass from the left, but his shot was high, wide and wasteful.
The Foxes were at least looking to make something happen and David Nugent nearly did with a curling effort that had everything bar direction, and that spurred Leeds into life with only the brute strength of Wes Morgan stopping substitute Dominic Poleon getting a shot in.
All of a sudden, the game was living up to its promise and Vardy forced the first save of the match with a 73rd-minute hit which Paddy Kenny parried, before the duo took each other on again with the goalkeeper quick off his line to put a clean-through Vardy off.
Wood then replaced Vardy and within minutes of his introduction the New Zealander produced the game's stand-out moment. He picked the ball up on the right and tortured the yellow-carded Pearce before giving him the slip and cracking a low drive against Kenny's left-hand post.
There was still time for Leeds to finally threaten after that, but Matt Smith was unable to direct a back-post header beyond Kasper Schmeichel.
The result leaves Leeds in eighth place in the embryonic table, one place above Leicester on alphabetical order.