Ukraine had five shots inside the first six minutes as they dominated from the first whistle, and Artem Kravets opened the scoring when he fired past Andrei Gorbunov after Maksim Volodko misjudged a long ball.
Yevhen Konoplyanka could have doubled the lead when he was denied by Gorbunov after meeting Andriy Yarmolenko's cross, but it was 2-0 on the half-hour when Yarmolenko tapped home opportunistically after the goalkeeper had intercepted Vyacheslav Shevchuk's cross.
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Ukraine wrapped the victory up before half time when Konoplyanka sent Gorbunov the wrong way from the spot after Mikhail Sivakov had barged over Kravets inside the penalty area.
The hosts continued to bombard the Belarus goal after the break but the visitors were handed a slim lifeline when Yevhen Khacheridi was adjudged to have impeded Sergei Kornilenko, and the forward picked himself up to convert from the penalty spot.
Ukraine's victory was tainted further when Denys Garmash received a second yellow card for simulation in the second minute of injury time, but it did not affect the result as Ukraine moved to within three points of top spot in Group C.