Karim Benzema and Cristiano Ronaldo both hit the post while Sergio Ramos was sent off as Real Madrid were held at Athletic Bilbao.
Zinedine Zidane’s champions needed a win to reduce the eight-point gap on leaders Barcelona, who drew 2-2 with Celta Vigo earlier in the day.
But Real were frustrated and efforts from Benzema and Ronaldo, with a clever volley, were as close as they came.
Real finished with 10 men after Ramos was dismissed for two bookings.
Ramos, dismissed for the 19th time in La Liga, had been booked for a foul on Raul Garcia when he caught Aritz Aduriz in the 86th minute and received his second yellow.
Real keeper Keylor Navas produced fine saves to keep out Inaki Williams and Aduriz.
Sergio Ramos, who was wearing a mask to protect a broken nose, was sent off for the 24th time in his career
This time last year Real were at the top of La Liga on 34 points from 14 games after Ramos’ last-minute equaliser at Barcelona in El Clasico.
The point in the Basque Country left them fourth in the table on 28 points from the same number of games
Meanwhile, Barcelona remain unbeaten at the top of La Liga after being held to an entertaining draw by Celta Vigo.
Iago Aspas put Celta ahead after Marc-Andre ter Stegen parried Maxi Gomez’s shot, but Barca levelled moments later as Lionel Messi converted Paulinho’s pass for his 17th goal this season.
Luis Suarez had a goal harshly ruled out for offside and Messi hit a post.
Suarez put Barca ahead from Jordi Alba’s cross after a Messi pass, but Gomez equalised from Aspas’ cutback.
Barca defender Samuel Umtiti pulled up with a hamstring injury while chasing Aspas for that goal, and has been ruled out for eight weeks.
The Catalan side are five points above Valencia, who visit Getafe on Sunday.