Matty Longstaff, Kell Watts and Tom Allan were part of the squad which reached the fifth round three years ago, but on Tuesday evening Neil Winskill's class of 2020/21 kept alive their dreams of winning the competition for the first time since a Paul Gascoigne-inspired United lifted the trophy in 1985.
Pat Jones gave the Terriers a 30th-minute lead, cutting in from the left and seeing his effort deflect off defender Harry Barclay to beat Oliver Marshall in the Magpies' goal.
But United levelled on the stroke of half time through a great low strike from Josh Harrison - who had earlier been denied by a superb last-ditch block by home captain Loick Ayina - after an incisive pass from Lucas de Bolle.
Newcastle were grateful to Marshall for a couple of good saves in the second period, but the hosts' goalkeeper, Nicholas Bilokapic, made a brilliant stop of his own in extra time to deny the lively Harrison a second of the night.
Marshall was called into action again in the 105th minute to keep out a Jones attempt but United finished the stronger of the two sides and with just two minutes of extra time remaining, an effort from Magpies substitute Josh Gilchrist hit a post.
Then Josh Scott also struck the woodwork in the final seconds as the tie went to penalties.
Nathan Carlyon, Tom Midgley, Gilchrist and Lewis Brannen all scored from the spot before Marshall saved from Conor Falls, allowing Reagan Thomson to coolly send United through to the fourth round with a 5-3 shoot-out win.
Newcastle United Under-18s: Oliver Marshall, Joe Oliver, Josh Scott, Nathan Carlyon, Harry Barclay, Lewis Brannen, Dylan Stephenson (Josh Gilchrist 105), Lucas de Bolle (Reagan Thomson 74), Josh Harrison, Elliot Anderson (c) (James Huntley 108), Joe White (Tom Midgley 100)
Subs not used: Piotr Banda, Jamie Miley, Josh Stewart