Zinedine Zidane's men now trail leaders Atletico, who thrashed Eibar 5-0 earlier in the day, by three points after the same number of games.
Third-placed Barcelona are two points behind Real with a game in hand.
Real, who were without a number of key players due to injury, suspension or Covid-19 isolation, were thankful for the woodwork and a fine display from goalkeeper Thibaut Courtois.
Mauro Arambarri spurned a good early chance for Getafe when he shot wide after 10 minutes before Jaime Mata headed against the post.
David Timor cleared a Mariano header off the line and David Soria kept out a Vinicius effort as Real threatened but Courtois saved brilliantly from Mata just before the hour.
Angel Rodriguez missed the target with another good chance for Getafe before having a deflected effort tipped away by Courtois.
Getafe also wanted a penalty late on after Rodriguez was challenged by Eder Militao but nothing was given.
Arambarri and Enes Ünal had chances in the latter stages for the hosts but missed the target.
Luka Modric had an opportunity to snatch victory for Real Madrid in added time but also failed to trouble the goalkeeper.