The visitors bossed the opening half and deservedly went ahead when Jose Antonio Reyes broke the deadlock on 40 minutes.
Reyes collected a neat pass from Ivan Rakitic before guiding the ball into the bottom-left corner from 12 yards.
Getafe levelled the scores just four minutes later courtesy of an Adrian Colunga free kick from all of 40 yards.
The 28-year-old forward, who until today had not scored since April 2012, found the bottom-right corner with an in-swinging delivery from close to the left touchline.
Getafe climb one place to 10th in the La Liga table, while Sevilla remain three points behind in 12th.