The stalemate at the Estadio Santiago Bernabeu leaves second-placed Real two points behind table-toppers Girona, and two ahead of Barcelona in third.
Athletic Bilbao are fifth after surviving a late Villarreal fightback to win 3-2 at El Madrigal, where Inigo Ruiz de Galarreta, Nico Williams and Inaki Williams had the visitors three goals up inside the opening half an hour.
Gerard Moreno and Alexander Sorloth scored in quick succession late on but Athletic held on.
A Pepelu penalty gave Valencia a 1-0 home win over second-bottom Granada, and it was the same scoreline as Alaves beat basement boys Almeria.
Roma pulled off a dramatic victory over Lecce at the Stadio Olimpico as two stoppage-time goals saw them come from behind to triumph 2-1.
Sardar Azmoun drew Jose Mourinho’s men level in the first minute of added time, cancelling out Pontus Almqvist’s goal, before Romelu Lukaku – who had had an early penalty saved by Wladimir Falcone – netted the winner three minutes later.
Lorenzo Colombo notched a brace as Monza won 3-1 at Hellas Verona, who are now in the relegation zone, with Cagliari moving out with a 2-1 home win over Genoa.
Nice returned to the top of Ligue 1, a point above second-placed Paris St Germain, with a 2-0 home victory over Rennes that saw both sides reduced to 10 men.
Jeremie Boga opened the scoring and a Steve Mandanda own goal added to that late on, not long after Youssouf Ndayishimiye had been sent off for the hosts and Warmed Omari then followed suit for Rennes.
Monaco are a point behind PSG in third after beating Brest 2-0 at the Stade Louis II, Denis Zakaria and Aleksandr Golovin getting the goals before Lilian Brassier was dismissed for the away side in stoppage time.
Reims are up to fourth after a Junya Ito goal earned them a 1-0 win at Nantes.
Rock-bottom Lyon secured a 1-1 draw at home against 16th-placed Metz thanks to Skelly Alvero’s late goal, while Le Havre won 2-1 at Toulouse and Strasbourg and second-bottom Clermont drew 0-0.
In the Bundesliga, third-placed Stuttgart suffered a second successive defeat, losing 2-0 at Heidenheim with Jan Schoppner and Tim Kleindienst on the scoresheet, and Wolfsburg were held 2-2 at home by Werder Bremen.