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Ukraine veteran and skipper Andrei Shevchenko became hero of the match after he headed two goals to hand all three points to his team.
Zlatan Ibrahimovic opened the score on 52 minutes, while Shevchenko netted brace on 55 and 62 minutes to help his team to secure victory.
Ukraine go top of Group D after the opening round of matches, following England's draw against France earlier on Monday.