The Ukrainians led just 36-35 at half-time but were never again threatened by England after outscoring them by nine points to zero to open a 53-45 lead in the next six minutes.
England were forced to make the trip without at least six first-choice players who made themselves unavailable either due to injury or other commitments. It was left to Colin Irish and Mark Hubbard, from League champions Worthing, to try and lift coach Kevin Cadle's team.
Irish led England's scorers with 18 points, supported by 14 from Hubbard and 12 from Guildford's Karl Brown.
In the other game in the group, Bosnia swamped Slovakia 97-68. England must now defeat both these two teams, beginning with Bosnia today, to take one of the top two places to progress to the second stage with the leading pairs from the other three groups.
At the end of the second stage, the top five will join the 11 nations which have already qualified for the finals which begin in Germany on 23 June.Reuse content