The Arsenal star was on hand to tuck home just before the half-hour mark in what was the games first shot on target.
Up until then, it had been a dreary game of football before Zinchenko lit up the Stadion Miejski Wroclaw, sending the Ukrainian fans into a frenzy.
England legend Stuart Pearce was on co-commentary for talkSPORT, who was critical of England's style of play.
He said live on air: "The Ukrainians really are a confidence-based side, and this will do that confidence no harm at all.
"England have had all the possession, but not really threatened the goal in any way, shape or form.
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"And Ukraine as the half has gone on, they've got more and more confident in their counter-attack threat.
"And they got big numbers in the box there and Zinchenko slid the ball in as it was pulled across the face of the goal."
But Ukraine's lead didn't last too long, as Kyle Walker popped up in the 41st minute to score his first international goal.
The Manchester City right-back was played in by Harry Kane with a delightful lofted through ball, with Walker then slotting the ball into the near post.
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The 33-year-old is playing his 77th cap for the Three Lions, an international career that has spanned 12 years after his debut in 2011 against Spain.
But the ball delivered by Kane was a thing of beauty as the striker sat almost between both centre-backs on the halfway line.
Like a quarterback, the Bayern Munich star pinged a pass over Ukraine's backline for an onrushing Walker, who tucked it in to make it 1-1.