Girona midfielder David Timor gave the home side a 16th-minute lead with a curled free kick from the edge of the box that nestled into the bottom corner.
Getafe looked for a way back into the contest, but they were mainly restricted to efforts from long range, as Pablo Sarabia saw his shot whistle over the bar from 30 yards.
The La Liga side did draw level in the 36th minute after a mistake by Girona goalkeeper Jorge Palatsi left Ciprian Marica with the simple task of tapping the ball home from close range.
Marica then had the chance to put Getafe ahead for the first time in the game in the 53rd minute, but the Romanian saw his shot creep just wide of the post.
Both sides had chances to win the match as the clock approached 90 minutes, with Jonas Ramalho being thwarted by a good Jordi Codina save.