They are six points ahead of sixth-placed Valencia, who visit Huesca later on Sunday.
Girona, who finished the game with 10 men, later sank into the relegation zone after Real Valladolid beat Athletic Bilbao 1-0 at home later on Sunday, leapfrogging the Catalan side to take 17th spot on 38 points to Girona's 37.
Getafe broke the deadlock in the 16th minute after a misplaced pass from Girona defender Bernardo invited a counter-attack and 37-year-old Molina fired into the bottom corner to score his 14th goal of the season.
Getafe coach Jose Bordalas had to watch from the stands as he was serving a touchline ban for insulting the referee in his side's 2-1 defeat at Real Sociedad which had threatened to derail their hopes of making the top four.
Girona's Borja Garcia was sent off in the 70th minute for dissent and Getafe made the most of their advantage when substitute Angel Rodriguez doubled the lead in the 77th, holding off two defenders before arrowing his finish into the net.
(Reporting by Richard Martin; Editing by Toby Davis and Ken Ferris)
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