A win would have put Manuel Pellegrini's side top on goal difference after Barca dropped their first home points of the season in a 1-1 draw with Villarreal on Saturday.
However, a gritty performance from Osasuna at their claustrophobic Reyno de Navarra stadium and Real's lack of creativity and penetration left the visitors two points adrift of the champions on 38 with 16 matches played.
Undefeated Barca have 40, Valencia, who beat visiting Espanyol 1-0 on Saturday, are third with 32 and Real Mallorca climbed above Sevilla.
A deflected strike from Julio Alvarez and a neat Aritz Aduriz chip gave Real Mallorca a 2-0 win over Athletic Bilbao in La Liga on Sunday to lift the Balearic islanders up to fourth.
After a forgettable first half at the Ono Estadi, Alvarez tried his luck from distance in the 49th minute and his shot looped up off the back of Athletic defender Fernando Amorebieta and over goalkeeper Gorka Iraizoz into the net.
Aduriz doubled the home side's lead on 65 minutes when he raced clear and chipped over the onrushing Iraizoz into the empty net.
Mallorca climb into the fourth Champions League spot with 30 points from 16 matches, the same as fifth-placed Sevilla, who squandered the lead and conceded in the fourth minute of added time to lose 2-1 at Atletico Madrid on Saturday.
Real Madrid can go top above Barcelona on goal difference with victory at Osasuna later on Sunday (2000 GMT) after Barca dropped their first home points of the season in a 1-1 draw with Villarreal on Saturday.
Pedro put the champions ahead in the seventh minute at the Nou Camp but David Fuster levelled six minutes after halftime to deny Pep Guardiola's side an eighth home win out of eight.
Barca have 40 points, with Real on 37 in second and Valencia, who beat visiting Espanyol 1-0 on Saturday thanks to a late Nikola Zigic header, are third with 32.
Elsewhere on Sunday, midfielder Francisco Casquero's late strike gave Getafe a 1-0 win over Real Valladolid which lifted the Madrid club to seventh.
Juan Manuel Lillo had a winning league debut as Almeria coach thanks to Jose Ortiz, whose superb long-range strike in the 89th minute snatched a 1-0 home win over fellow Andalusians and bottom club Xerez.
Mid-table Sporting Gijon drew 2-2 with relegation-threatened Malaga and sixth-placed Deportivo Coruna were held to a 0-0 draw at struggling Real Zaragoza.