Eduardo Vargas gave the hosts a dream start when he headed in the opener after seven minutes, but Getafe responded by scoring twice in three minutes through Angel Lafita and Ciprian Marica, before Pedro Leon made sure of the points with a late finish.
Valencia defender Jeremy Mathieu took issue with the way the midfielder celebrated the goal - which the Frenchman thought should have been ruled out for offside - and responded by appearing to hit Leon in the face.
That earned Mathieu a red card and forced Valencia to play the final few minutes of the match with 10 men, although Getafe had all but secured the victory by that late stage.
Valencia put pressure on their struggling visitors from the off and it paid dividends when Vargas rose to head home from a corner.
But despite the poor start, Getafe soon found a foothold in the game.
Marica caught sight of goal twice in the space of a minute, causing problems for Vicente Guaita on both occasions but unable to beat the Valencia keeper.
Although Marica's efforts did not lead to a goal, they galvanised the visitors, and the next time Getafe attacked, they scored.
Lafita raced towards goal from the left hand side but had two defenders ahead of him, and just as he got to the box, arrowed the ball between the legs of Philippe Senderos and in off the far post.
Getafe had failed to score in either of their previous two matches but just moments after netting for the first time in 223 minutes, they had the ball in the net again, Marica beating the offside trap to send a diving header past Guaita.
Valencia sought an immediate response and almost pulled level straight away, Dani Parejo heading a cross from the left onto the crossbar.
And the hosts were cursing the woodwork in the second half too, Paco Alcacer hitting the bar from inside the area.
Before then, Getafe stopper Jordi Codina had made three fine saves to keep his side in front, saving a team-mate's blushes by averting an own goal, and then punching clear a header from Senderos.
Valencia's hopes of getting something from the game were crushed when substitute Mehdi Lacen spotted a gap in the home defence and released Leon, who controlled the ball under pressure from Mathieu and shot into the bottom corner before celebrating wildly.
And he appeared to mock Mathieu, who responded by pushing his hand into Leon's face with the former Real Madrid player subsequently crashing to the floor. That earned Mathieu a red card while new Getafe coach Cosmin Contra was also sent off for arguing with the referee as tempers threatened to boil over in the closing stages.