The European nation were facing a play-off against Iceland to see if they could make the summer tournament.
Mudryk got the winner for Ukraine in the 84th minute to seal a vital 2-1 win, after they had initially fallen behind.
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Ukraine president Volodymyr Zelenskiy said on Telegram: Thank you boys!
Thank you to the team! For proving once again that when Ukrainians face challenges but refuse to give up and continue the fight, they invariably win."
Ukraine played the game in a neutral, but full of Ukrainian supporters, Wroclaw Stadium in Poland on Tuesday.