The hosts stormed back from conceding a 19th-minute opener to Alvaro Negredo and finished strongly with four goals in the second half.
Miguel Torres levelled in the 35th minute before Mehdi Lacen put Getafe in front three minutes after the break.
And Miku then netted twice either side of a Pedro Rios effort as the hosts scored three times in nine minutes to humiliate their opponents.
The win lifted Getafe level with their opponents on 45 points.
Sevilla went into the game on the back of a 3-0 win over Real Zaragoza, but it was the hosts, smarting from last week's humbling by Barcelona, who started well with Miku firing over the bar in the ninth minute.
Sevilla responded with Manu bringing an excellent fingertip save out of Getafe keeper Miguel Moya in the 18th minute and one minute later the visitors took the lead when Negredo converted a cross by Piotr Trochowski.
Moya blocked a shot by Jesus Navas as Sevilla threatened to extend their lead before Getafe equalised, Torres volleying home in style from a Rios corner.
Jaime Gavilan forced a save out of Javi Varas as the game swung in Getafe's direction, but Sevilla should still have regained the lead moments into the second half when Negredo shot over from six yards.
The hosts were made to pay as Lacen put Getafe in front in the 48th minute and the hosts extended their lead just past the hour mark when Miku slid home from a Rios ball into the box.
It was 4-1 in the 68th minute when Rios headed home a cross by Mane, and 5-1 just two minutes later when Miku grabbed his second from a ball in from the right by Rios.
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