Switzerland beat European champions Portugal 2-0 in their opening World Cup 2018 Group B qualifier on Tuesday.
Breel Embolo and Ahmed Mehmedi scored first-half goals for the hosts, who had Arsenal midfielder Granit Xhaka sent off in stoppage time.
Portugal were missing Cristiano Ronaldo, with the Real Madrid forward injured since July's Euro 2016 final.
Beaten finalists France got their own campaign off to a slow start with a 0-0 Group A draw in Belarus.
Elsewhere in that group, Sweden held the Netherlands to a 1-1 draw with a Wesley Sneijder goal cancelling out a chip from Marcus Berg.
Bulgaria beat Luxembourg 4-3 thanks to an injury-time winner from former Aston Villa winger Aleksandar Tonev.
Former Everton boss Roberto Martinez won his first competitive match as Belgium manager with a 3-0 victory in Cyprus.
Martinez's side had been booed by some Belgian fans after a 2-0 defeat by Spain in a friendly last week, but a double from Toffees striker Romelu Lukaku and a late third from Yannick Carrasco gave them three points.
Despite the win, they are third in Group H after the first round of matches.
Edin Dzeko was among the scorers as Bosnia-Herzegovina hammered Estonia 5-0, while Greece eased to a 4-1 win over Gibraltar in Portugal.
Cahill keeps going
In Asian qualifying, former Everton midfielder Tim Cahill came off the bench to give Australia a 1-0 win over the United Arab Emirates.
The 36-year-old drilled home a cross from Bournemouth's Brad Smith with his first touch after coming on.
The Socceroos made it two wins from two games to go top of Group B, ahead of Saudi Arabia, who beat Iraq 2-1 in a game that was played in Malaysia because of security issues in Iraq.