Goals in each half from Xabi Alonso, on his 100th international appearance, sent the world and European champions into a semi-final with Iberian rivals Portugal in the same Donbass Arena stadium on Wednesday.
"I think we had things well under control throughout," said Alonso. "It was never going to be easy but I thought we played a great match."
It was Spain's first competitive win in seven attempts against France, who were bidding to become the first team to eliminate Spain from a major tournament since the French side that reached the 2006 World Cup final.
French winger Frank Ribery tirelessly pushed the Les Bleus attack, curling in crosses, running through the Spanish back-line. Laurent Blanc's side had no option but to be patient. The French, however, looked threatening during the second half trying to match their opponents but none of their attempts tested Spain's stopper Iker Cassillas.
Spain, for the first in the tournament, allowed their opponents to dominate in the second period but raced forward on the counter-attack. Their passing style worked perfectly despite criticisms back home.
"I don't think it was an unfair result because they didn't really have any chances. We were in control most of the time. Matches like these are very intense and you have to concentrate very hard to win," said Spain coach Vicente del Bosque.
While Spain can now contemplate the prospect of facing the in-form Cristiano Ronaldo, France return home after fulfilling their objective of reaching the last eight, only to fall short against the world's top national side.
"Is a quarter-final France's level at the moment? I don't know," said France coach Laurent Blanc. "What I do know is that the best sides will be in the semi-finals, and France won't be." In an attempt to nullify Spain's attacking threat, Blanc opted for a conservative 4-5-1 formation, with right-back Mathieu Debuchy lining up in an unfamiliar right-wing role ahead of Anthony Reveillere.