After Roberto Soldado had smashed the visitors in front in only the fifth minute, Getafe quickly hit back through a Pedro Rios header.
Miku headed Geta into the lead before a comical Bruno own-goal put them 3-1 up before the break.
The first half was a fast, flowing affair, with Diego Castro forcing an early save from Vicente Guaita moments after Rio saw a long-range strike whistle over the bar.
A minute later the ball was in the other goal. Jonas flicked deftly through for Soldado with the outside of his right foot and the striker notched his 16th league goal of the season with a thunderous finish into the near-post top corner.
On 12 minutes Getafe were right back in the game: Castro played Jaime Gavilan down the left and his cross to the near post was perfect for Rios to head home.
Valencia have been hit-and-miss of late and lost their previous match at home to Real Zaragoza. However they continued to play the ball confidently and work it intelligently in the final third: when Jonas scooped him in again, Soldado lifted the ball beyond the diving home centre-half Cata Diaz before trying to do the same to Miguel Angel Moya, but the keeper - on loan from Valencia - got enough on it to prevent a goal.
In the 24th minute Geta were ahead. Rios's long cross from the right was stabbed into the ground by Gavilan and when the ball dropped into the danger area, there was Miku to score his eighth goal of the season with his head.
And on the half-hour mark they doubled their advantage: Gavilan delivered a free-kick from the right which came off Bruno and looped over Guaita into the far corner.
Los Che came out for the second half fired up - so much so that Jordi Alba immediately talked his way into a yellow card and Pablo Piatti followed him into the book soon after for a cynical foul.
Valencia spent the remainder of the match looking to open up Getafe, but the home side were as content as ever to sit and defend and threaten on the counter knowing that they had a two-goal lead.
Unai Emery's side should have had a penalty when Diaz had a fistful of Victor Ruiz's shirt inside the box and the game descended into injuries and substitutions late on to frustrate the Valencia coach.
Valencia in third remain only three points ahead of local rivals Levante - who they next play in La Liga after their Europa League first leg against AZ Alkmaar - and Malaga, and have now played a game more than both.
Levante host Osasuna on Sunday while Malaga travel to Espanyol.