Trent Kone-Doherty struck in the 90th minute to hand the hosts the win.
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With the three points, Liverpool now have a place in the knockout phase of the tournament.
Reds coach Rob Page again handed Prince Cisse a start at the back, with the youngster being the son of former Liverpool striker Djibril Cisse.
Highly-rated teenage striker Josh Sonni-Lambie was also in the starting line-up on the day.