Alberto Bueno headed in Gael Kakuta's lobbed pass for what proved to be the winner in the 20th minute. It was the forward's sixth goal of the season.
Rayo rose to 11th place, while Celta was left in seventh after its first loss in six away games this season.
Later, Valencia visits Levante in a city derby, Villarreal hosts Almeria and bottom side Cordoba is at Elche.
Banners supporting Rayo's decision to help an 85-year-old woman who had been evicted from her apartment were seen in the stands at Vallecas Stadium.
"Let's see if we can all help (her) if we work together," said Rayo goalkeeper Cristian Alvarez.