Last year's finalists dominated the game from the start but were only able to score once, when Sarabia struck from close range in the 12th minute following a low cross by Marcos Llorente.
After a mistake by the Swiss defence, the Atletico Madrid winger found Sarabia ghosting in between two opponents inside the six-yard box and he scored with a first-time shot.
Spain have five points from their opening three Group A2 matches to sit two behind leaders Portugal and two ahead of third-placed Czech Republic.
Switzerland have suffered three consecutive losses and are winless in their last five games since qualifying for this year's World Cup.
Spain host the Czechs in Malaga and Switzerland entertain Portugal in Geneva on Sunday.
Spain coach Luis Enrique made eight changes in the starting team that struggled to a 2-2 draw with the Czech Republic last time out.
Llorente and Sarabia were the main focus of Spain's attack with their pace, fed by precise passes from teenager Gavi behind the Swiss line.
Spain enjoyed almost 70% of possession, but forwards Alvaro Morata and Ferran Torres lacked the precision to make it pay.