The result put them on 18 points with one game left, two ahead of second-placed Scotland, who had also already qualified and were held to a 2-2 draw in Georgia.
Spain manager Luis de la Fuente rested several regular starters at lowly Cyprus and his second-string team were rarely bothered by the locals, with 16-year-old Lamine Yamal opening the scoring from close range after dribbling past a defender and the keeper in a fine effort in the fifth minute.
“I saw the goalkeeper in front of me and I cut back until I was alone. Happy to help the team and for the beautiful goal,” Yamal said.
It was Yamal’s second goal with Spain, after the Barcelona wonderkid became the country’s youngest international and goals corer aged 16 years and 57 days as he made his debut away to Georgia in their Euro 2024 qualifier last September.
Real Sociedad captain Mikel Oyarzabal struck with a tidy finish under the goalkeeper’s legs in the 22nd minute to double the advantage, but had to wait for the confirmation from the VAR as his effort was first ruled out for a suspected offside.
As the visitors took their foot off the gas pedal after the break, Kostas Pileas netted the consolation goal in a counter attack late in the second half.
“To play football is very difficult and it’s difficult to win comfortably, scoring a lot of goals,” said De La Fuente.
“The opponent also play and they want to please their fans, so we need to be focus all the time.
“In the second half we didn’t play as well as we did in the first and they had their chances later on. That’s a lessons we should learn.”