The Foxes, who came into the match with a six-game unbeaten run, were defeated thanks to a goal in each half from Magpies striker Adam Armstrong, although a late Adam Dawson strike did briefly raise hopes of a City comeback.
Steve Beaglehole’s side had begun the match in a positive manner – midfielder Michael Cain posing the biggest early threat, firing wide before forcing a great stop from Jak Alnwick soon afterwards.
Harry Panayiotou also saw an effort drift off target before England Under-17 international, Armstrong, gave the home side the lead not long before the break. He latched on to a Jonas Gutierrez pass to drill a low shot beyond the reach of City ‘keeper Adam Smith.
In a fairly even encounter City also saw Jacob Blyth, who had recently returned from a productive loan spell with Northampton Town, go close, but the all-important second goal eventually fell the way of Peter Beardsley’s Magpies.
Armstrong again found himself in the right place at the right time to apply a nice sweeping finish to Tom Heardman’s pass, making it 2-0 with just 15 minutes remaining.
The Foxes rallied however, with Alnwick forced into a good save before exciting winger Dawson cut inside and produced an excellent finish to pull a goal back for City.
There was almost to be a fairytale finish in stoppage time when City goalkeeper Smith came up for a corner only to see his glancing header drift just wide of the post, meaning the north-east side go into the hat for the last-eight draw.
Newcastle: Alnwick, Streete (Morgan 46), Good, Dummett, Gillesphey, Gilliead (Roberts 62), Bigirimana, Olley, Jonas, Armstrong, Quinn (Heardman 76)
Subs not used: Mitchell, Kemen
Goals: Armstrong 38, 76
City: A. Smith, Pearson, Elder (Taft 65), Paratore, Sesay (c), Kennedy (Frempah 80), Dodoo, Cain, Blyth (Barrington 65), Panayiotou, Dawson
Subs not used: Sharpe, Anton
Goal: Dawson 83