With Cristiano Ronaldo among a host of names missing out due to suspension, los Blancos were decidedly off-colour in front of goal, and struggled to create many meaningful moments in the face of a determined rearguard effort from the hosts.
Substitute Kaka's 76th minute red card effectively ended any hopes of a victory for Madrid, who could see the gap between them and league leaders Barcelona grow to 18 points should the Catalans triumph against Malaga on Sunday.
Sergio Ramos and Antonio Adan joined Ronaldo on the sidelines through suspension, meaning that Gonzalo Higuain, Jose Callejon and Iker Casillas were all handed starts by Jose Mourinho.
It took the visitors the best part of half an hour to register their first real chance. Andres Fernandez rashly strode off his line to confront Higuain, who beat him to the byeline, but saw his cross towards an empty net hacked away from danger by Alejandro Arribas.
Madrid seemed unable to find any conventional route through to goal, and it took an unorthodox header from Callejon, that looped onto the roof of the net, for them to threaten the home side again.
Osasuna were generally comfortable in defence and managed to create some danger of their own at the other end of the pitch, when Alvaro Cejudo smashed a half volley just over the bar after combining well with Emiliano Armenteros.
But the visitors would spur a great opportunity to break the deadlock on the stroke of half-time. Fernandez was caught out of position again, this time by Callejon, who teed up Fabio Coentrao to drive his finish wide of the far post from the edge of the box.
The Navarrans went close barely a minute into the second half, as Kike Sola cut in off the left flank and forced Casillas into his first save of the match with an awkward parry.
And as the second half wore on, the hosts looked increasingly capable of repelling the threat posed by Madrid, who were having a tough time breaking through their ranks.
Kaka and Karim Benzema entered the fray just before the hour mark, and the Brazilian picked up a booking within minutes of his introduction for a flying tackle on Oier.
And that incident would come back to haunt him in the 76th minute, as he was shown his second yellow card after reacting angrily in a confrontation with several Osasuna players, reducing Madrid to 10 men.
The dismissal effectively signalled the end of Madrid's ambitions for all three points, as they were forced to hang on for the remainder of the match and limp towards a point that they barely deserved.