The City man stole in to tap home from close-range before the hour after Andriy Yarmolenko’s effort had been diverted back into his path.
And the result was put beyond doubt with ten to play when Artem Dovbyk doubled the visitors’ advantage.
Ukraine, who are aiming to qualify for only their second World Cup, started the evening third in European Group D, two points behind Finland in the race for a play-off spot.
But a combination of the Finns’ 2-0 defeat to group leaders France and Zinchenko’s decisive contribution means Oleksandr Petrakov’s side progress to the final round of qualifying.
While Zinchenko and co.’s route to the play-offs was far from clear cut, the Ukrainians went unbeaten throughout their Group D campaign, drawing an incredible six of their eight matches and winning the other two.
Kevin De Bruyne was also on target for Belgium in their 1-1 draw with Wales in Cardiff.
Roberto Martinez’s side had already secured their spot at the Qatar World Cup, but were keen to end their Group E campaign on a high with victory over their second-placed opponents.
And they got off to the dream start when the City midfielder showed quick reactions to roll in the opener at Danny Ward’s near-post after the ball ricocheted into his path on the edge of the box.
But the hosts, knowing a point would guarantee them a play-off spot, responded after the half-hour when Kieffer Moore pounced on a miscued Arthur Theate clearance.
De Bruyne was still in the thick of the action as Belgium pushed to regain their lead, almost grabbing an assist four minutes after Wales’ equaliser when his corner was headed wide by former City man Dedryck Boyata.
And the midfielder went close once again to grabbing a spectacular assist before the break when he found Thorgan Hazard on the edge of the box, but the winger’s sumptuous side-footed volley came crashing back off the post.
Martinez’s men, who enjoyed 76% possession throughout proceedings, continued to pile the pressure on the hosts but, urged on by a vocal Cardiff City Stadium crowd, Wales held on for their all-important point.
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Elsewhere, Nathan Ake was a late substitute for Holland as they finished top of Group G thanks to a 2-0 win over Norway in Rotterdam.
Oranje were locked in a three-way horse race with their opponents and Turkey for an automatic place in next year’s winter tournament but knew they would be guaranteed first place with three points.
And Louis Van Gaal’s side achieved exactly that, with late goals from Steven Bergwijn and Memphis Depay ensuring their spot in Qatar, while consigning Turkey to the play-offs and Norway to third.