Wolves looked as if they would progress as they went two goals up early in the second half through goals by Bruno Jordao and Renat Dadashov.
But Joe Hardy netted his third Liverpool goal since joining from Brentford this month, before 16-year-old Harvey Elliott's sensational overhead kick levelled the scores in front of 4,400 fans at Molineux.
A STUNNING Harvey Elliott acrobatic strike 😱— Liverpool FC (@LFC) January 30, 2020
🙌 Our U23s will now face @VfLWolfsburg_EN in the PL International Cup quarter-final, after yesterday's dramatic fightback: https://t.co/XUEpi9PyHm pic.twitter.com/PScphFkSpB
Liverpool, Paris Saint-Germain and Athletic Bilbao all finished on four points in Group E, but the Reds progressed as winners by virtue of goals scored.
Wolves finished bottom after three draws.
The draw for the last eight will be made later today and published on @PLYouth on Twitter.