Getafe were reduced to 10 men in the 25th minute of the match when Mauro Arambarri picked up his second yellow card in the space of four minutes.
However, the home side scored in the 66th minute through Markel Bergara, and resisted pressure from the previously-unbeaten Los Che in the latter stages to continue their impressive start to the 2017-18 campaign.
A win for Valencia would have taken them to within two points of the league leaders Barcelona, but the defeat means that Marcelino's side remain five points off Ernesto Valverde's table-toppers after 14 matches of the season.
Getafe sit eighth, just two points off sixth-placed Villarreal, after winning five, drawing four and losing five of their 14 fixtures this term.
Valencia will attempt to return to winning ways when they host Celta Vigo next weekend.