Ukraine are third on 15 points, three behind leaders Spain who moved ahead of second-placed Slovakia by virtue of a better head-to-head record thanks to a 2-0 win over their closest rivals later on Saturday.
The Ukrainians visit Slovakia on Tuesday.
Ukraine took the lead after seven minutes when a defensive blunder from their midfielder Maxim Volodko allowed Artem Kravets to race into the penalty area and beat the keeper with a low shot into the far corner.
Visiting keeper Andrey Gorbunov denied the hosts numerous goal-scoring chances in the first half but could not prevent Ukraine doubling their lead after 30 minutes when he diverted the ball into the path of Andriy Yarmolenko who steered it into the empty net from close range.
Sevilla's new signing Yevhen Konoplyanka scored the third from the penalty spot four minutes before halftime after Mikhail Sivkov brought down Artem Kravets following a corner.
Belarus striker Sergei Kornilenko netted a consolation from the penalty spot in the 62nd minute before Ukraine's defensive midfielder Denys Garmash received a second yellow card and was sent off in stoppage time for diving, ruling him out of Tuesday's match.
(Reporting by Igor Nitsak; editing by Toby Davis)
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