Javier Camunas broke the deadlock with a shot off the post in the 62nd minute of a typically bruising battle at the Reyno de Navarra stadium.
Mourinho responded by throwing new loan signing Emmanuel Adebayor into the fray, but they were unable to find a way past a side who had not won in their previous eight games.
Real’s second defeat of the season left them second on 51 points from 21 games, behind Barca with 58 after the champions won their 15th consecutive match 3-0 at Hercules on Saturday.
“There are still a lot of points available, we have to keep on fighting,” Real midfielder Xabi Alonso told Spanish television. “It’s always a difficult place to play and we knew the first goal would be vital, it fell to them and that made it even harder.”
Real struggled to create chances and missed the guidance of Alonso, who started on the bench as he recovered from the flu. Karim Benzema and Cristiano Ronaldo had good opportunities saved by Osasuna’s Ricardo Lopez, but the abrasive Navarrans were a constant threat.
A long punt downfield found its way through for Camunas to score after an hour, and Real responded immediately throwing on Adebayor, Kaka and Alonso.
Despite Real’s late pressure it was Osasuna who came closest to scoring again, Krisztian Vadocz having a shot blocked on the line by Alvaro Arbeloa. Osasuna climbed to 16th, three points above the relegation places.