All the goals came in a frantic first half. Adrian Colunga opened the scoring for the hosts after 10 minutes but Augusto Fernandez equalised just 10 minutes later, before Diego Castro and then Federico Fernandez added goals of their own before the break.
Before the match Celta coach Paco Herrera said his aim was to keep a clean sheet and stamp out his team's habit of conceding goals from crosses, so he is likely to be furious with how his team surrendered their three goals due to poor defending.
Getafe looked the more determined team from the start and deserved to take the lead. Celta defender Gustavo Cabral, who had already presented Getafe with their first chance of the game, surrendered the ball to Abdel Barrada in midfield, and the Moroccan passed to Colunga, who struck a left-footed shot past Javi Varas.
The visitors gave their sizeable and loud travelling support something to cheer about when Augusto Fernandez headed in a cross from left-back Roberto Lago to draw level.
If the goal was somewhat against the run of play, Getafe soon sought to make up for it, with Varas having to save from Barrada and then Colunga shortly after the equaliser.
Barrada and Colunga were the standout performers on the pitch and the latter played a crucial part in restoring his team's advantage.
Pedro Leon broke down the right-hand side to square the ball to Colunga, whose shot was blocked on the line by a Celta defender but bundled home by Diego Castro.
Colunga then missed a good chance to grab his second goal, sending a shot high and wide when through on goal but Getafe's third goal would come soon enough.
Centre-back Fernandez appeared unmarked at the near post to head in a corner to give the Madrid side a two-goal advantage going into the break.
Luis Garcia's side were happy to surrender the ball to the visitors in the second half but the Galicians could not make their superior possession count, and it was Getafe who came closer to scoring again, with Colugna, Barrada and substitute Jaime Gavilan all squandering chances.
The result means that Getafe move 12 points clear of the relegation zone and will have their eyes on the Europa League places.
Celta have recorded just one league victory in 2013 and with four coaches being dismissed since the Primera Division took its winter break in December, Herrera has reason to fear he could be the fifth.