Goals from Juan Albín and Javi Casquero gave Geta all three points on Matchday 1.
Although the Azulones were under pressure at the outset, they in fact managed an early goal as Albín seized on a goalkeeping error to finish from close range.
Diego Castro equalised with a volley late on in the first half, and with chances at both ends the second half seemed to be heading towards a draw.
However, Casquero surfaced right at the death with a trademark long-range strike to seal all three points for the visitors.
Videos when available.
Sporting: Sergio Sánchez; Sastre, Ivá Hernández, Jorge, Canella; Matabuena, Míchel; Pedro (Morán 80), Quique Mateo (Bilic 70), Diego Castro; Barral (Carmelo 70).
Getafe: Pato Abbondanzieri; Cortés, 'Cata' Díaz, Mario, Licht (Granero 64); Guerrón (Contra 80), Casquero, Celestini, Gavilán; Albín, Manu (Soldado 64).