(CNN) -

Belgium set a date with the U.S. in the last 16 of the World Cup as the curtain fell on the gripping group stages in Brazil, while Algeria celebrated a historic first.

Thursday's 1-0 victory over South Korea was more than enough for the unbeaten Belgians to advance from Group H as winners, despite having a man sent off.

As their red and yellow clad fans celebrated in Sao Paulo, there were similar scenes of jubilation in Curitiba.

The U.S. and Belgium will face off at 4 p.m. ET on Tuesday.

Algeria made history in Brazil, reaching the knockout stages of the global tournament for the first time at the expense of Russia.

"Les Fennecs" -- the Desert Foxes -- will need all their wiles as they face the might of Germany next.

Germany had consigned the U.S. to a 1-0 defeat in Thursday's earlier matches but Team USA escaped from a grueling Group G -- which also featured Ghana and Portugal -- on goal difference.

Belgium might think themselves lucky to march into the knockout stages with their unbeaten record intact after being forced to play more than half the match with 10 men.

Steven Defour was sent off for a rash studs-up challenge on the cusp of halftime and South Korea sniffed blood, pressing forward after the break.

But if the statistics tell us anything about Belgium, it is never count them out.

Breaking upfield, defender Jan Vertonghen picked up the rebound of Divock Origi's fizzing effort to break the deadlock after 77 minutes.

Belgium's last six World Cup goals have been scored in the last 20 minutes of the match. Team USA better be prepared for a lively finish.

Algeria had arrived in Sao Paulo buoyant from their 4-2 victory over South Korea -- their first World Cup win in 32 years.

When Russia took an early lead in the must-win showdown, a fairy tale ending for Vahid Halilhodzic's side had seemed a remote possibility.

Aleksandr Kokorin, who is nicknamed "Bieber" because of his youthful similarity to the Canadian pop star, was soon on song.

He rose brilliantly to power home Dmitry Kombarov's cross after just six minutes and from there Russia looked intent on protecting their lead.

But Algeria, cheered on by the undiminished enthusiasm of their fans, were not done yet.

When a free kick was swung into the box, the Russian defense rocked and Islam Slimani headed into an open goal with 60 minutes on the clock.

The draw was enough for Algeria to join Nigeria as the second African side in the last 16.

Meanwhile, Russia will be hoping to find answers before hosting the next World Cup in 2018.

After failing to qualify for the 2006 and 2010 editions of the global football fiesta, the Russians have now fallen at the first hurdle in 1994, 2002 and 2014.

The remaining 16 nations in the World Cup will enjoy a rest day Friday before the footballing fever gets even hotter on Saturday.

Hosts Brazil face a tricky Chile side for a place in the quarter-finals while Colombia take on Uruguay, now rendered rather toothless by the ban for biting striker Luis Suarez.

The controversial Liverpool player is not the only star name to take an early flight from Brazil.

Portuguese star Cristiano Ronaldo and Spain's defending champions were among the big guns saying adeus from Brazil.