The visitors appeared on course for a regulation victory when they eased into a 2-0 lead inside half an hour through Carlos Bocca and Alberto Moreno.
However, they were shocked by goals in the 81st and 84th minutes from Mateus Manucho and Patrick Ebert as the hosts somehow clawed their way back into a game Sevilla had completely dominated.
Getafe profited from Granada defender Pape Diakhate's first-half dismissal to claim a fourth successive win and move up to fifth place.
A Jeison Murillo own goal and Pedro Leon's third strike of the season shortly after half-time sealed a 2-0 win to continue Getafe's flying start.
Ten-man Elche survived a late onslaught from Real Betis to record their third win in a row with a 2-1 result.
The visitors scored twice in quick succession in the first half through Manu del Moral and Fidel Chaves, but Jorge Molina's goal put Pepe Mel's side back in contention before the break.
Dominga Cisma was sent off early in the second half for a second yellow card but, even with an extra player, Betis' search for an equaliser proved elusive.
A late free-kick from Alejandro Galvez gave 10-man Rayo Vallecano a 1-0 success at Almeria.
The centre-back struck on 78 minutes to put the Madrid side ahead, only 15 minutes after Saul Niguez had been sent off for two bookings.