Title rivals Atletico Madrid and Barcelona played out a 0-0 draw at the Vicente Calderon as Athletic Bilbao hammered Almeria.
Valencia suffered a surprise defeat away by lowly Celta Vigo, while Sevilla snatched a late point on their travels against Elche.
Barcelona remain top of the Primera Division after their top-of-the-table clash with Atletico Madrid failed to live up to its billing and finished goalless.
Lionel Messi and Neymar started the game on the bench and, even when both emerged in the second half, neither were able to give their side an attacking edge against a highly-disciplined Atletico outfit.
Though the result changes little for either side involved, the draw will be welcomed by Real Madrid, who can close the gap on their two title rivals to three points with a win at Espanyol on Sunday.
Two goals by Brazilian striker Charles earned Celta Vigo a valuable 2-1 win against Valencia in their bid to avoid relegation from the top flight.
Valencia took the lead in the 23rd minute when Dani Parejo headed in from close range from a right-wing cross by Sofiane Feghouli.
Celta were level five minutes into the second half when Charles scored from close range after being set up by Rafinha.
With 12 minutes to go Celta got the goal their pressure warranted when Charles shot powerfully into the top corner from 20 yards.
Athletic Bilbao tightened their grip on a UEFA Champions League spot with a resounding 6-1 victory at home to Almeria.
Midfielder Mikel Rico opened the scoring with just six minutes played and Ander Herrera doubled the lead just four minutes later.
Aymeric Laporte made it 3-0 just after the half-hour mark, but Helder Barbosa gave Francisco Javier Rodriguez's side faint hope by scoring before half-time.
However, further goals from Aritz Aduriz put the hosts further ahead and a double from substitute Ibai Gomez completed the rout.
Daniel Carrico headed a last-minute equaliser as Sevilla salvaged a 1-1 draw away to Elche.
The home side had taken an 82nd minute lead when Fidel's left-wing cross was glanced home by fellow substitute Cristian Herrera.
Elche were denied an important win in the final minute, though, when Jose Antonio Reyes curled in a cross from the right and Carrico stooped unmarked to head home at the near post.