The hosts dominated possession but neither side managed to prove incisive in the final third, with little goalmouth action to be seen at either end of the pitch.
The result leaves Getafe in eleventh, three points away from Real Betis in eighth place but just a point ahead of Valencia in 14th.
Alaves, on the other hand, sit in the relegation zone, three points clear of bottom-placed Huesca but level on points with 17th-placed Osasuna.
Huesca’s victory at Real Valladolid on Friday night means that there’s just ten points separating bottom from ninth in a congested bottom-half of the table.
Getafe face a tough forthcoming triple-header. They play Sevilla in Seville, travel to Valdebebas to face Real Madrid and then host Real Sociedad.
Alaves host Real Valladolid next, before travelling to Catalonia to play Barcelona and then to the Basque Country to face La Real.