Gonzalo Higuain showed strength and power to hold off a Getafe defender and slot home from close range.
Madrid created more opportunities to add to their advantage and will disappointed to not be further ahead after some wasteful finishing.
Mest Ozil was the chief culprit, somehow managing to hit the woodwork unmarked from four yards.
Cristiano Ronaldo also looked dangerous for much of the first 45 minutes, coming close with a long-range strike.
The reigning La Liga champions will be confident of securing their first win of the campaign if they can continue to control the match in the second half.