Valencia ends winless home drought
The hosts got off to the perfect start and were 2-0 up inside seven minutes as Roberto Soldado headed in from Sofiane Feghouli's cross before the Valencia captain turned provider to set up Jonas to curl past Miguel Angel Moya.
Getafe soon had a foothold in the game, though, as Alvaro Vasquez turned in Xavi Torres' pass from a narrow angle, but Valencia restored their two-goal advantage on the half-hour as Ricardo Costa powered home a header from Tino Costa's corner.
Alexis reduced the deficit once more on the hour mark with another fine header, this time from Abdelaziz Barrada's corner, but as Getafe pushed for an equalizer they only succeeded in leaving space at the back and Valencia finally sealed the three points when Nelson Valdez swept home Jonathan Viera's cutback in stoppage time.
Consecutive home defeats had seen Valencia fall seven points off the pace in the race for the final Champions League place, but they ensured a perfect end to an up-and-down 2012 with a blistering start.
Soldado took his tally for the season to 13 with a neat finish in the first minute after Feghouli broke free down the right and dinked a cross into the heart of the area.
The Spain international then showed signs his partnership with Jonas could be returning to the heights it hit last season as they exchanged passes on the edge of the area before the Brazilian slotted the ball into the top corner.
Six minutes later Getafe had one back as Torres broke through a couple of challenges in midfield and fed Vasquez, who finished expertly to register only his second goal since joining from Espanyol in the summer.
Diego Castro then wasted a great chance to bring the visitors level as he blazed over from close range after 24 minutes, and they were punished almost instantly as Ricardo Costa took advantage of very slack marking to head home from an inswinging corner.
Jonas and Feghouli then got in each other's way as they spurned a great chance to make it four.
Both sides spurned great chances just after the break as Alvaro was denied by Diego Alves before Jonas was denied by a post after being played through again by Soldado.
Valverde's men were then guilty of poor defending from a corner as Alexis scored against his former club, but they continued to threaten a fourth goal and, after Pablo Piatti and Costa went close, they finally made the game safe when Valdez stroked into an empty net from Viera's unselfish cross.