Two second-time goals ensured that Ukraine secured maximum points in Group H over Moldova, leaving them four points behind England.
The home nation had the best chances of the opening half, with Oleg Gusev trying to break the deadlock courtesy of a header from the centre of the box, but his effort missed the target.
Minutes later Andriy Yarmolenko attempted a left-footed shot from outside the box, but the chance was saved, and Ukraine were unable to find the breakthrough.
The home nation continued to knock on the door in the second half, and their efforts were eventually rewarded with a goal from Yarmolenko, who guided a shot from the centre of the box into the left corner of the net.
They doubled their lead with a header from Yevhen Khacheridi, while Moldova replied late in the second half with a left-footed shot into the bottom corner courtesy of an assist from Anatolie Doros.
Despite finding the back of the net, it was a consolation goal for Moldova, who relinquished maximum points.