The home game played in Lviv saw empty stands due to COVID-19 restrictions.
Ukraine National Team have opened this season with a win as it edged past Switzerland in Nations League's Group A where Germany and Spain also played the same night, sealing a draw.
The 2:1 win thus put Ukraine on top of the group.
West Ham's Andriy Yarmolenko opened the score with a cheeky backheeler just 14 minutes into the match, while Switzerland equalized just before break with a long-range effort by Haris Seferovic.
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Manchester City's Oleksandr Zinchenko eventually curled home a left-foot beauty from almost an impossible angle, sealing the win for Andriy Shevchenko's squad.
Celebrating the goal, Zinchenko held up his black armband, payin respects to the team's late doctor who recently passed falling victim to coronavirus.
The home game was played in Lviv, seeing empty stands due to COVID-19 restrictions.