Marcelino Garcia Toral's men, who had won four of their previous five games, started brightly and deservedly went ahead on 19 minutes in spectacular fashion.
After the game had become open and both teams had wasted chances, the hosts levelled 10 minutes before half time. Pedro Rios's out-swinging corner found Miguel Torres unmarked in the six-yard box and the former Real Madrid full-back emphatically volleyed home.
Following an even first half, Getafe dominated the second period and took the lead four minutes after the restart. Mehdi Lacen collected Diego Castro's pass on the right touchline before cutting in and drilling a low left-footed drive from 20 yards.
Miku put daylight between the side on 63 minutes with a calm finish from 10 yards after an excellent through ball from Rios.
Rios then put the game beyond doubt with a 69th-minute header before Miku got his second two minutes later, by almost exactly the same method as his first.
Sevilla are now ninth in the La Liga table, level on points with Getafe and six points behind fourth-placed Malaga.