Moments later the home fans' frustration grew when midfielder Arambarri was shown a second yellow card and dismissed in the 25th minute.
Getafe went ahead in the 66th minute through a distance shot from midfielder Markel Bergara which took a big deflection off former Arsenal defender Gabriel Paulista and sailed over goalkeeper Neto and into the net.
Valencia, who were missing decisive winger Goncalo Guedes and defenders Ezequiel Garay and Jeison Murillo through injury and whose coach Marcelino was serving a touchline ban, struggled to create chances.
Their best efforts came from a series of free kicks from captain Dani Parejo, who struck the post and was three times denied by former Valencia goalkeeper Vicente Guaita.
Getafe's goalkeeper made one final save to thwart his old side in repelling a shot from winger Carlos Soler deep in injury time.
Valencia midfielder Parejo criticised the poor playing surface at Getafe's Coliseum Alfonso Perez stadium after his side's first defeat under Marcelino.
"They took the three points but if you want to see great football then you can't play on a pitch like this," Parejo told reporters.
"They have beat us playing on a pitch in terrible conditions and that's not fair, but that's football. We knew it would be difficult and we have to congratulate Getafe.
"The ball couldn't move properly, the pitch was dry and it seems like they haven't looked after for it for a week. It's no excuse but we have to look for solutions if we want to be considered the best league in the world."
Valencia squandered the opportunity to profit from Barca's 2-2 draw at home to Celta Vigo on Saturday. They remain in second place, five points behind the Liga leaders, who have 36 after 14 games.
Marcelino's side are only one point ahead of Atletico Madrid in third and three above Real Madrid and Sevilla who are fourth and fifth respectively.
(Reporting by Richard Martin; editing by Clare Fallon)
