The Russian side managed to find the breakthrough in the 15th minute of the contest as Oleg Shatov nudged the ball into the back of the net from close range.
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The Russian managed to ease through Valencia's defenders, causing a shock to the Spanish side, who tried to make things happen through Paco Alcacer, but his final touch was missing.
There were numerous offside calls in the first half, but two of them - one for each side - were wrongfully flagged, providing a frustrating few moments for the teams on show.
One offside call, which was correctly flagged, would have been welcomed for Axel Witsel as he missed an open goal after the ball was fizzed across the area.
Valencia returned to the pitch after the break knowing that they needed to score at least two goals to give themselves a hope of progressing, but it was the Russian side that started the second half on the frontfoot.
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However, with around 20 minutes before the final whistle, Danny received the ball off a one-two with Shatov before squaring it to Dzyuba, who tapped the ball past the keeper and into the back of the net.
Valencia had too much of a mountain to climb to get back into the contest, particularly after they lost Ruben Vezo to a red card in the 82nd minute after denying Shatov a goalscoring opportunity.
Should Gent claim victory over Lyon this evening, then Zenit will drop to second and the Belgians will go top.