Ukraine were whistled by their own fans near the end of the first period but responded after the restart with goals from Artem Kravetsk, Denys Germash and Evhen Konoplyanka.
The win move Ukraine level on 12 points with European champions Spain, who visit Belarus later on Sunday, and three points behind group leaders Slovakia who host Macedonia.
Bottom side Luxembourg almost scored after 10 minutes when winger Daniel Da Mota hit the post with only goalkeeper Andriy Pyatov to beat after evading Mykola Morozyuk's sliding tackle.
Ukraine's Taras Stepanenko headed over the bar from close range a few minutes earlier and later Konoplyanka applied a poor finish inside the penalty area to a neat Andriy Yarmolenko pass.
However, Ukraine finally took the lead four minutes into the second half when striker Artem chested the ball into the net after Kravetsk Morozyuk curled over a cross from the right.
Germash grabbed their second goal in the 57th after defender Vyacheslav Shevchuk's headed the ball into the area having been the first to react when his initial shot was blocked.
Konoplyanka rifled a low shot inside the post in the 86th to wrap up the win after stealing the ball following careless defending to cap what was a frustrating overall performance.
Luxembourg remain last in the group with one point.
(Editing by Ken Ferris)
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