The 36-year-old Molina netted his fourth goal in four games, less than 10 minutes after coming off the bench.
"It was just a small step, but a very important one, especially because we didn't concede any goals," Getafe midfielder Francisco Portillo said.
Getafe, one of the surprises in the Spanish league this season, was near full strength while Valencia played without many of its regular starters. The second leg is next week in Valencia.
"It's still completely open," Valencia goalkeeper Jaume Domenech said. "Playing at Mestalla (Stadium) will be key for us."
Four-time defending champion Barcelona visits Sevilla on Wednesday with coach Ernesto Valverde set to rest Lionel Messi and other top players.
On Thursday, Real Madrid hosts Girona and Real Betis visits Espanyol.