The “Nati”, as the team is known, managed to frustrate hosts France, who also go through to the knockout stage as top of Group A.
Despite a lack of goals the game was not without its exciting moments.
Goalkeeper Yann Sommer had the 15,000 Swiss fans in the stadium holding their breath as the French came close to scoring three times, each time hitting the woodwork.
Swiss midfielder Valon Behrami punctured the ball with one of his studs, and several shirts were ripped in the match in Lille on Sunday night.
Trainer Vladimir Petkovic changed the line-up slightly for the third game in the group round, replacing Haris Seferovic with teenage striker Breel Embolo.
The team took on and mastered their greatest challenge to date, after upping their game in successive matches, tabloid Blick reported.
“They made the match an experience, they excited us and they showed us their potential,” it said in a commentary.
Petkovic had finally stepped out of the shadow of his predecessor veteran Ottmar Hitzfeld, the paper said.
“After two difficult years we have ‘our Nati’ back. A team we can be proud of.”
Switzerland’s next game is on Saturday in St Etienne where they will come up against Germany, Poland or Northern Ireland.