The Andalucian hosts started the better of the two teams, with Jesus Navas narrowly missing the target from close range in the sixth minute.
Three minutes later Federico Fazio went close with a header from a Jose Antonio Reyes cross.
The Seville outfit continued to dominate proceedings and eventually went ahead in the 34th minute when Fazio headed home Ivan Rakitic's cross.
It became 2-0 to Sevilla four minutes later when Alvaro Negredo successfully converted a penalty.
Sevilla's next league match is against Granada away next Sunday, while Getafe will host Real Madrid on the same day.