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They secured the berth as one of the best third-placed teams after finishing Group C with one win and two losses.
They beat Guatemala 4-2 in the opening match thanks to goals from Nguyen Minh Tri and Tran Van Vu but lost the next two matches against Paraguay and Italy.
Depending on the draw, Vietnam can face Russia or Portugal in the knockout game.
The championship has attracted the participation of 24 teams and will conclude on October 1.
World No 4 Italy is one of the title favourites in this World Cup. They won a bronze medal in Thailand in 2012, in Brazil in 2008, and were also runners-up in Chinese Taipei in 2004.
Meanwhile, Vietnam rank 39th in the world.
VNA