The Vietnamese had advanced to the Round of 16 before the final game in Group H, with Iran being the remaining rivals.
The Southeast Asian team beat Iran 4-1 on September 15 while Kyrgyzstan drew 1-1 with the Iranians on September 18.
With two victories, Vietnam, led by Japanese coach Toshiya Miura, topped the group. They will take on UAE in the next round on Friday.
Kyrgyzstan won the other ticket of the group to the last-16 round thanks to a better goal difference in comparison with Iran.
They scored one goal and conceded two whereas the Iranians netted two goals but had five against them. Both teams earned one point after the group stage.
As promised before the Vietnam-Kyrgyzstan clash, Miura enrolled his best players for the starting line-up to target a win over Kyrgyzstan.
Both sides displayed an equal performance by exchanging attacks during the game. They mainly competed for the ball in the middle of the field, though.
Several clear chances were created in the first half but no goal was scored.
In the 62nd minute, Vietnamese midfielder Vu Minh Tuan crossed a flying pass in front of the Kyrgyzstan box and defender Baimatov Azamat manipulated the ball with his hand in the penalty area.
Tuan successfully converted the penalty shot into the winning goal for Vietnam.
The Round of 16 is scheduled to begin on September 25.
Twenty-nine teams have been playing in the men's football event meant for under-23 players. Group A to Group E have four teams each, while each of Group F, G and H consists of three teams.
The 17th Asiad is taking place from September 19 to October 4 in Incheon.
Team Vietnam ranks eighth on the medal tally of the Games, with one gold, two silvers, and four bronzes.
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