Getafe, who lost to Sevilla in the 2007 final, started the match brightly at a rain-lashed Sanchez Pizjuan.
Striker Manu del Moral twice went close but was denied first by home goalkeeper Andres Palop and then by a well-timed challenge from Adriano Correia.
The visitors were finding it all too easy to control possession and Sevilla coach Manolo Jimenez replaced striker Alvaro Negredo with midfielder Ndri Romaric just after the half hour.
Despite the complaints of the home fans, the change appeared to have the desired effect and Getafe keeper Oscar Ustari had to be at his best to keep out a close-range Fabiano volley in the 41st minute.
The Brazilian striker found the net in first-half added time, nodding over Ustari from Adriano's cross, and sprinted to the bench where he donned a black sombrero in homage to club president Jose Maria del Nido.
A mazy run from winger Jesus Navas led to a second for the home side with 10 minutes left. The Spain international burst into the penalty area and his low centre ricocheted into the net off the hapless Alvarez.
Atletico Madrid host Racing Santander in their last-four first-leg match on Thursday.
