Alexia Putellas grabbed a goal either side of half-time and an assist as the Spaniards put Switzerland to the sword in Zurich.
The match was the team's first since FIFA announced on Monday that former Spanish football chief Luis Rubiales had incurred a three-year ban for his forced kiss on Jenni Hermoso.
If the news had any impact on the players, it was soon forgotten as Oihane Hernandez gave them the lead after four minutes, which Putellas then added to seven minutes later.
The world champions piled the misery on the hosts after the break, adding five goals, Alayah Pilgrim grabbing a consolation strike for the Swiss.
Star midfielder Aitana Bonmati was present for the occasion despite picking up the Ballon d'Or on Monday in Paris.
Switzerland, on the other hand, have endured a difficult start in a tough group, going down to four consecutive losses.
- England in trouble -
World Cup runners-up England slipped to a 3-2 defeat in Leuven that puts their Nations League hopes in the balance.
It was the first time that England have conceded three goals since Sarina Wiegman took over as coach in 2021.
Laura de Neve curled in a free-kick to give Belgium the lead on nine minutes, only for Lucy Bronze and Fran Kirby to put England back in charge.
The home side were level, though, before half-time through their captain Tessa Wullaert who struck deep into first-half additional time.
When Georgia Stanway was penalised for handball five minutes from time, Wullaert calmly put away the penalty to secure the win for Belgium.
The European champions languish third in Group A1 on six points, three behind leaders Netherlands who won 1-0 in Scotland.
Herve Renard's side lacked inspiration but were denied three times by the post as well as some good saves by Norwegian goalkeeper Aurora Mikalsen.