Sustained first-half pressure by a dominant Sociedad told when Vela hit the back of the net in the 31st minute after pouncing on a loose ball in the six-yard box.
Two minutes later, the 23-year-old Mexico striker hit his fifth goal of the season with a skillfully struck right-footed shot from outside the area.
“The most important thing for us is team cohesion, not individual play, and today has been a good match for us,” said Vela. “Playing at home always gives us an extra edge.”
Mikel Gonzalez slotted home Sociedad's third in the 61st before Gonzalo Castro added another in the 77th minute.
Sociedad rises to ninth place in the standings on 16 points, the same as Rayo, which is 11th in the standings.
Sociedad midfielders Asier Illarramendi and Ruben Pardo were dominant, leaving Rayo looking ragged and unable to string passes together.
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