Beaten 1-0 at Feyenoord in their Group A opener, Jose Mourinho's side struggled to break down their unadventurous Ukrainian opponents until the introduction from the bench of Wayne Rooney.
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The England captain's mishit shot was headed in by Ibrahimovic to leave United a point behind group leaders Fenerbahce, who visit Old Trafford on October 20.
"It was difficult," said Mourinho. "We had our chances in the first half. We could have scored and it would have been a different match. But we didn't. They kept organised and had plenty of players behind the ball, but with players ready to do something on the counter-attack. It was difficult and we needed to win.
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"One week, three defeats. One week, three victories. But I was not depressed by the defeats and I am not over the moon with three wins."
It was a far from fluent performance from United, but it maintained their upturn in form following the recent run of three straight defeats that had destroyed their early-season momentum.
Zorya, UEFA group-phase debutants, became United's 100th continental opponents, and the result did not disappoint the visiting team’s manager, who revealed that he is happy with the performance of the players.
"I was very happy with my guys' performance," said beaten manager Yuriy Vernydub, whose side are currently second in the Ukrainian Premier League. "We played at the same level as Manchester United. In my eyes the game was a draw, because the goal was a bit of a silly one."
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