City loanee Pablo Maffeo nearly gave the hosts a dream start when he cut inside and drilled a low effort which cannoned back off the post on the 11th minute.
Real Madrid could be facing an injury blow at the back after Raphael Varane was withdrawn at half-time against Girona.
Getafe offered little going forward in the first half but were a different side after the interval and deservedly equalised after 78 minutes as Francisco Portillo's superb pass allowed fellow substitute Angel Rodriguez to control on his chest before firing home.
Despite going a goal behind, Girona did not look discouraged and they almost hit back in the 35th minute when Portu rattled the woodwork from close range.
However, Girona nearly grabbed a third, Stuani dinking the ball past Casilla and just wide of the post.
Yet, rather than mount a late comeback as they did so often on route to a first La Liga and Champions League double for 59 years last season, Madrid looked short of energy and ideas in the final half hour as Girona held out for a famous victory.
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