Joaquin Larrivey then crashed a shot against the post as Rayo came close to breaking the deadlock. Roberto Trashorras and Iago Falque also fired wide as the visitors produced the better football in the first half.
Navas was in action again soon, keeping out Trashorras's free kick, before Larrivey drilled a shot wide of the post.
David Barral had a rare chance for the hosts, but wasted it as he lifted his effort over the bar.
Both sides tried to find the winner in the second half, but the quality in the final third was poor.