A Nabil Touaizi goal on the stroke of half-time gave City the lead, but Liverpool struck back late on through Duncan - to take an evenly-matched contest to extra-time and penalties for just the third time in the history of the competition.
Cole Palmer smacked City's second penalty against the crossbar while every other taker scored, with Paul Glatzel thumping home the decisive spot-kick to record a 5-3 victory in the shootout.
Spanish striker Touaizi, 18, joined City's youth ranks from Valencia in 2017 and has managed 11 goals from 23 appearances in all competitions.
However, his strike was cancelled out by the Reds' own young forward as City goalkeeper Louie Moulden produced a howler to allow 17-year-old Duncan's late effort to slip through his fingers and force the game to extra-time.
The striker actually spent seven years in City's academy system, having joined from Wigan Athletic in 2011, before switching to Liverpool last summer, where he has scored prolifically, hitting a whopping 24 goals and recording seven assists from 33 appearances in all competitions this season.
The two dominant forces in English football at present went head-to-head at youth level as well, with Liverpool emerging victorious in what they hope will be a foreshadowing of their Premier League title challenge, despite being a point behind Pep Guardiola's outfit with three games left to play.
The Spanish tactician was in attendance and his imprint was clearly visible as City dominated the ball and produced some lovely link-up play, but there were a few occasions in which Liverpool's high press forced errors as they tried to play out from the back as both sides mirrored the style of their senior squads.
City reached the final via matches against Clevedon Town, Nottingham Forest, Derby County, Bournemouth and West Brom, while Liverpool overcame Portsmouth, Accrington Stanley, Wigan Athletic, Bury and Watford.
The Reds are now four-time winners of the tournament, having lifted the cup in 1996, 2006 and 2007, while Manchester City have won it twice before, in 1986 and 2008.