Three second-half goals steals three points for Getafe and leaves Sevilla without a home win in two attempts.
Frederic Kanoute gave the home team the lead with a simple finish in the first-half but it was to be the catalyst for the Azulones' spirit in the second. Manu drew the visitors level from the spot early in the second period. Just minutes after Miku gave Getafe the lead with impressive composure and a rocket from Pedro Rios ensured three precious points.
Getafe created a wonderful chance to break the deadlock within just two minutes. Miku played the ball in behind Sevilla and Manu del Moral rounded keeper Andres Palop, but could only steer his shot into the side netting from a tight angle.
Sevilla also threatened early on. Diego Capel got lucky with a misplaced pass and whipped a high curling cross towards Diego Perotti but the winger couldn't help it back towards a white shirt. Another low drilled cross was just out of reach of Kanoute with the Getafe defence caught napping.
Pedro Rios was left with a cut eye when challenging Didier Zokora in the air, the Ivory Coast international unintentionally catching the midfielder with an elbow.
Kanoute and Negredo came close to linking-up in spectacular style, the later heading back across goal to his strike partner. Kanoute shaped to hit an acrobatic overhead-kick from eight yards but couldn't direct it on goal.
Abdoulay Konko had a clearer opportunity to finish a volley from the edge of the six yard box which he couldn't turn on goal. That was followed by Romaric and Diego Capel in quick succession missing from inside the box.
Despite some hesitant defending by the visitors they did look threatening going forward. Captain Manu tested Palop with a missile from distance that just went wide.
Sevilla's spell of pressure leading up to the half-hour mark finally paid dividends. Romaric showed good determination to chase and turn over a useful cross from the left. Cata Diaz failed to clear the danger and effectively controlled the ball for the arriving Kanoute, who made no mistake in finding the net.
The physical battle in the centre of the park was being shaded by Romaric and Zokora and it made things difficult to respond to going behind for Getafe.
Los Azulones did create a couple of shooting chances just before the break but couldn't test Palop between the sticks for Sevilla.
Sevilla took a few minutes to establish themselves in the second-half but once they did los Nerviones began in search of a crucial second. Negredo and Martin Caceres both coming close.
Manu should have equalised seven minutes after the break. A simple and quick move found the captain clean on goal and Palop got down well to make a fantastic save. Palop could however do little with Miku's effort just a minute later, his side-foot shot from close range smashing off the bar.
Just two minutes later Getafe had a penalty after Ivan Marcano's header came off Konko's arm. Palop got a firm hand to Manu's spotkick but the penalty trickled in off the post to the anger of the Sevilla glovesman.
Getafe completely turned the game on its head before an hour had been played. Gavilan's cross was expertly controlled by Miku, who turned inside Fernando Navarro and smashed his volley past Palop.
Frustration for the home fans continued. Kanoute finding Negredo in the box but the striker turned to see the flag after hitting the corner of the net with his shot, and it was ruled out.
Perotti fell culprit to selfishness in the box for the hosts. The Argentine blasting his shot straight at Jordi Cordina with Kanoute screaming free to the left of the winger.
The game was sealed with just over ten minutes to go. Pedro Rios unleashed an absolute beauty into the roof of the net after latching on to a rebound from a corner. The shot leaving Palop again with no chance.
Sevilla continued to try find a way back into the contest but were left empty handed attack after attack, ending Getafe's poor run without a win to lift their aspirations for the rest of the season.