Remo Freuler sealed Switzerland's 3-2 win in their grudge match with Serbia to snatch a last 16 spot as the Qatar World Cup group stage concluded with another spectacle on Friday.
Brazil had already qualified but ended up top despite a late 1-0 loss to Cameroon, who bow out along with the Serbians.
The defeat for a second-string Brazil means no team won all their group games in Qatar.
The Swiss will now face Portugal on Tuesday, with Brazil taking on South Korea the day before.
It is a third straight last 16 qualification at the World Cup for Switzerland, who took the lead through Xherdan Shaqiri and levelled for 2-2 thanks to Breel Embolo.
The first knock-out round line-up is now complete with eight European sides, two South American teams, two from Africa, three from the Asian Football Confederation including Australia, and the United States.
