Spain fell 2-1 at Slovakia in Group C for its first loss in a qualifier for the European Championship or World Cup since 2006.
Paco Alcacer appeared to have sparked Spain's comeback in the 82nd, only for Miroslav Stoch to catch its defence off balance with a counterattack with 3 minutes left.
England had no such trouble against minnow San Marino, rolling to a 5-0 win in Group E. Wayne Rooney, Danny Welbeck, Phil Jagielka and Andros Townsend scored for England and Alessandro Della Valle added an own goal.
In Group G, Sweden drew 1-1 at home with Russia.
The second batch of Euro 2016 qualifiers continues through Tuesday.
Spain's run of 14 away victories in qualifying was in danger from the 17th minute when Iker Casillas awakened concerns over his form that started at a disappointing World Cup.
Once so reliable, Spain's goalkeeper couldn't punch out Juraj Kucka's powerful free kick that flew straight at him, letting it glance off his fists and into the net.
Coach Vicente del Bosque recently began a so-called renewal of Spain by bringing in new and younger players. But none of them started and Spain's short-passing game built around a Diego Costa who prefers to run in open spaces was unable to finish its chances until Alcacer went on.
Alcacer slipped behind defender Martin Skrtel to pull in Jordi Alba's pass and level in the 82nd.
But Slovakia caught Spain seeking the winner with only two defenders on the pitch as Stoch raced forward to head in Marek Hamsik's cross three minutes from time, sending the home fans into raptures.
"That's football," Del Bosque said. "We aren't going to blame any individual players."
Slovakia became the only team in Group C to win its first two games.
Spain was left level on three points with Macedonia and Ukraine after they both rebounded from loss in their first matches.
Macedonia's Besart Abdurahimi scored in injury time to grab a 3-2 win at home over Luxembourg, while Ukraine scored twice late to win 2-0 at Belarus.
England routing San Marino 5-0 was no surprise, a 60th consecutive loss for world football's co-lowest-ranked side. But Switzerland sitting bottom with zero points after two games is surprising.
Switzerland, which reached the World Cup round of 16 in Brazil, followed up last month's loss to England by going down 1-0 at Slovenia. Milivoje Novakovic scored an 80th-minute penalty after Switzerland defender Johan Djourou brought down Kevin Kampl.
At the top, England has a superior difference to Lithuania, which beat Estonia 1-0 on Saulius Mikoliunas' late goal.
At Wembley, San Marino did prevent England from scoring until the 24th minute through Jagielka's header, but Rooney extended the hosts' lead before half time from the penalty spot. Welbeck and Townsend netted after the break before Della Valle scored an own goal from Rooney's cross.
Russia heads a trio of teams on four points after being held to 1-1 in Sweden. Level on points with the Russians are Austria, which beat Moldova 2-1 away, and Montenegro, which failed to defeat tiny Liechtenstein in a goalless draw.
The Swedes languish in fourth with two points after the draw with Russia followed an opening-day draw in Austria. They are without a win in three competitive fixtures dating to their failed attempt to reach the World Cup.
Sweden went behind after 10 minutes when Artyom Dzyuba set Alexander Kokorin free behind the Swedish defence, and the striker slotted the ball past Andreas Isaksson with a low shot from outside the box.
Sweden missed a good chance to respond almost immediately when Sebastian Larsson's penalty was saved by Igor Akinfeev.
Toivonen brought Sweden level in the 49th, finishing from close range off a left-wing cross from Durmaz.