Clinical first-half strikes by Dominic Corness and Stefan Bajcetic put the contest in the Reds' control and they sealed a big three points at the Academy through Woltman and James Norris after the interval.
The result lifted Marc Bridge-Wilkinson's side above Porto in the Group B table by virtue of their head-to-head record, with both teams on 10 points ahead of the final fixtures next month.
A win at AC Milan next month would now guarantee the Reds progress to the last 16.
Liverpool U19s: Mrozek, Bradley, Beck (Chambers, 85), Quansah, Koumetio, Bajcetic, Gordon, Corness, Woltman, Norris, Frauendorf (Musialowski, 70).
Unused substitutes: Davies, Cannonier, Mabaya, Clark, Miles.
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