Pablo Sarabia has scored seven goals and provided two assists for Spain since June 2021, more than any other player
Sarabia slid home Marcos Llorente's cross in a goal which was allowed to stand after a video assistant referee review for offside.
The Swiss had two late chances in Geneva, with Breel Embolo lobbing wide and Djibril Sow's last-second volley being blocked.
Spain are on five points from three games in Group A2.
Portugal - who beat the Czech Republic 2-0 - are two points clear of their neighbours.
-- Courtesy of BBC Sport