Valencia, who are enduring a difficult season and sit ninth in La Liga, failed to create many openings with substitute Denis Cheryshev ruled offside before he tested Getafe keeper Leandro Chichizola.
Molina eventually found the breakthrough, controlling the ball deep in the box and then rifling home to hand Getafe the advantage ahead of next week's second leg at Valencia's Mestalla stadium.
"We've only taken a little step, but it was important to keep a clean sheet," said Getafe midfielder Francisco Portillo.
"It was a tough game, an even game, I think everyone's work is undeniable and that is the key for this team. It's important to go there with a good result."
(Reporting by Rik Sharma; Editing by Toby Davis)
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