The Scottish champions won all three group of their games, scoring 10 goals and conceding none, and have made next week's knockout draw for a fourth successive season.
Each of City's players made a contribution to the win over the at the Exclesior Stadium, but none more so than 19-year-old Fiona Brown. She scored the goal of the game and provided assists for the other three. Eddie Wolecki Black's decision to field virtually a reserve team against Glentoran on Monday also paid off handsomely last night against a jaded Zhilstroy team.
"We were fresh and able to set the tempo of the game high," said the City head coach. "Zhilstroy relied on the same group of players for three games in six days and that is tough. Qualifying for a fourth successive season is a tremendous achievement. We're going to go into the draw as 13th seeds, so once again we'll avoid any of the big hitters in the last 32."
It did not take long to establish that City were by far the more accomplished side as they took a grip of the game quickly, going ahead after just nine minutes. Brown and Jo Love combined to set up a chance for Leanne Crichton, although her low side-footed shot should have been saved by Zhilstroy captain Iryna Sanina. However, the goalkeeper spilled the ball and as she floundered Denise O'Sullivan stepped in to accept the gift.
The early goal changed the complexion of the tie completely but it became apparent that Zhilstroy, who needed just to draw to reach the last 32, did not have a Plan B.
The Ukrainians had little about them to suggest why they had won their opening two group games easily. Their uncomfortable afternoon got worse when Brown provided the cross for Love to beat Sanina with a downward header.
As in the opening two games, the standard of City's crisp, fast-moving outfield play was far superior to anything their opponents could muster, even if further goals did not arrive until the second half.
The third goal of the match, a stunning individual effort from Brown, was worth waiting for. She cut in from the right to strike a fierce left-footed shot past Sanina from 20 yards. "I saw where the keeper was standing and just went for it," said Brown.
City made it four just before the hour mark and again Brown was involved in the build up. She knocked Abbi Grant's cross into the path of O'Sullivan to score from close range.
Striker Susan Fairlie thought she had scored a fifth in the 75th minute but French referee Florence Guilleman decided her header from Brown's cross had not crossed the line. Even so, City's superiority was emphasised when they had the luxury of bringing on 15-year-old substitute Carla Boyce, who made a starting debut against Glentoran.
In the other group game, the team from Northern Ireland defeated Slovakians Nove Zamky 5-2.