Dortmund, meanwhile, have been on a sizzling run since losing to RB Leipzig on Sept. 10, scoring 20 goals in four straight wins against Legia Warsaw in the Champions League and Darmstadt, Wolfsburg and Freiburg in the Bundesliga.
Dortmund, who thrashed the Polish club 6-0 away in their opening group game, are second in the German top flight and on Friday equalled a club record of 24 games without defeat at home in the Bundesliga with a 3-1 win over Freiburg.
Even in the midst of Real's sensational winning run, Zinedine Zidane's side were criticised by the media for unconvincing performances and their sloppiness was punished by Las Palmas in their last La Liga outing.
Midfielder Tana hooked home a poor clearance from Real's Raphael Varane to cancel out Marco Asensio's opener and, after Karim Benzema had restored Real's lead, Sergio Araujo sneaked into the box from the left to level in the 85th minute.
Real's lacklustre displays have been compounded by the absence of midfield anchor Casemiro and influential left back Marcelo through injury and the form of talisman Cristiano Ronaldo.
Ronaldo has endured a difficult start to the season, scoring twice in four games -- including against his former club Sporting in Real's 2-1 home win in their first Champions League group game - while missing three due to injury and illness.
He reacted angrily to being substituted by Zidane with 18 minutes left at Las Palmas.
Striker Alvaro Morata, however, said there were still plenty of reasons to be optimistic.
"We still haven't lost and we are still top of the league. The important thing is how you finish and we have to win all our games if possible," he told reporters on Saturday.
"We have to keep working and now focus our minds on the Champions League."
Eleven-times European champions Real have a dismal record in Germany, having won four out of 30 competitive games in the country, and have lost their last three visits to Dortmund.
Dortmund are waiting on the fitness of their Spain centre-back Marc Bartra and Colombian forward Adrian Ramos, who both missed Friday's win over Freiburg.
Their hitman Pierre-Emerick Aubameyang finished the game with a knock although the Gabon striker, who has four goals in his last three games, said it was nothing to worry about.
(Reporting by Richard Martin; editing by Ken Ferris)
