As the Swiss secured second place, Group E leader England made it nine wins out of nine in qualifying, with Theo Walcott and Raheem Sterling scoring in a 2-0 win over Estonia on Friday.
With one qualifier remaining, Switzerland has an unassailable five-point advantage over Slovenia, which was held 1-1 by Lithuania but is almost certain to make the playoffs.
Slovenia has a three-point advantage over fourth-place Estonia and goes into the final qualifier at winless San Marino with a plus-nine goal difference.
"That's important because it fluctuates with the FIFA rankings and I'm only hoping I've not been misled that we are now safe to be seeded," England coach Roy Hodgson said.
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England will have to be far more ruthless at Euro 2016 than at Wembley Stadium against Estonia.
Sterling didn't add England's second goal until the 85th minute of a low-quality game, sliding in to meet Jamie Vardy's cross and put the ball in the net.
England was without injured captain Wayne Rooney, whose only appearance on the field was before the game to collect a golden boot from Bobby Charlton after breaking his England scoring record by netting for a 50th time in last month's win against Switzerland.
Against San Marino, Michael Lang put Switzerland in front in the 17th minute but the floodgates only opened in the second half with Gokhan Inler's penalty after 10 minutes.
There were further successful spotkicks from Johan Djourou and Breel Embolo and goals from open play from Admir Mehmedi, Pajtim Kasami and Eren Derdiyok.