Villarreal went searching for a victor and nearly found one through Japanese teenager Takefusa Kubo, who is on loan from Madrid, but Courtois stood firm to make the save.
Zinedine Zidane's side were missing seven players through injury and illness, including the indispensable trio of Sergio Ramos, Karim Benzema and Casemiro, but the champions went ahead in the second minute with a diving header from Mariano Diaz.
"It's not a good point", the Frenchman said after the match. The French coach has this to say: "We deserved much more from today's performance, especially in the first half".
The last time neither of the two giants of Spanish football, Barcelona and Real Madrid, were not leading after the ninth matchday was in 2006, when Sevilla topped the table by one point from Barcelona, with Real fourth. "It was a bit of everything".