Joe Brayson fired the Toon teenagers into an early lead at Whitley Park, turning the ball home from Trevan Sanusi's cross, before Michael Mills' composed finish doubled United's advantage towards the closing stages of a dominant opening 45 minutes from Chris Moore's side.
Harry Howell's penalty halved the deficit for Albion on the stroke of half-time but the hosts held firm in the closing stages of the third round tie to secure their place in round four of the prestigious youth competition.
The hosts were unfortunate not to break the deadlock inside the opening 60 seconds as Sean Neave, a representative of England at under-18 level, rose high from Leo Shahar's lofted cross from the right flank but directed his headed attempt onto the underside of the crossbar.
In the ninth minute, Newcastle took the lead through Brayson's smart finish as the teenage forward, son of former Magpies striker Paul, latched onto Sanusi's teasing pass, who managed to beat Cristiano Anah to a loose ball in the build-up, before the former stroked a precise first-time effort into the bottom right-hand corner.
Mills, who joined the Magpies' youth set-up from Port Vale in the summer of 2023, went close to doubling the hosts' lead as the 15-year-old winger, who primarily plays on the left flank, dangerously cut inside following a bursting run into the box before his fiercely driven effort was bravely blocked by Brighton defender Freddie Simmonds.
Newcastle's youngsters struck the woodwork for a second time as teenage defender Luke Craggs leapt from Shahar's corner at the back post before guiding his header onto the corner of the bar.
Brayson was unable to double his and United's goalscoring tally before the half-time break as the 17-year-old, who signed a two-year scholarship with his boyhood club last year, attempted a speculative lob from distance but, despite lifting the ball over Albion goalkeeper Alfie Mansell, directed his attempt wide of the target.
Newcastle's youngsters doubled their lead in the 41st minute as Mills completed a clinical counter-attack, racing clear on goal following Neave's threaded through ball before cooly dispatching the ball into the bottom right-hand corner.
United's two-goal cushion, however, was halved on the stroke of half-time, as Howell converted from the penalty spot, placing the ball beyond Magpies goalkeeper Aidan Harris, who initially brought down Callum Mackley inside the box, from 12 yards.
Harris produced a key stop to prevent Nehemiah Oriola from levelling the cup clash after the Albion winger raced in behind the United backline, following Jacob Vickers' defence-splitting pass from his own half, but the Magpies 'keeper stood tall to block the drilled effort.
The Houghton-le-Spring-born teenager, who celebrates his 18th birthday next week, was forced into action shortly after, holding Howell's first-time effort inside the box after United lost possession in a dangerous position before keeping out Oriola's stinging drive minutes later.
Neave went close to netting his ninth goal of the season at under-18 level as the 17-year-old striker, who scored on his full Premier League 2 debut in a 3-1 win against Leeds United Under-21s last month, darted forward and, after twisting and turning to evade his marker, saw a powerful drive turned out for a corner by Mansell.
Despite five minutes of stoppage-time, Newcastle's youngsters saw the contest out against their Seagulls counterparts to seal their spot in round four for a fifth successive season, maintaining their hopes of lifting the trophy for a third time in the club's history.
Newcastle United Under-18s: Aidan Harris, Leo Shahar (c), Logan Watts, Luke Craggs, Jake Durrant (Sam Alabi 63), Rory Finneran, Anthony Munda, Trevan Sanusi, Michael Mills (Matheos Ferreira 70), Joe Brayson (Thomas Bryant 63), Sean Neave.
Subs not used: Henry Johnson, Adam Harrison, Matthew Taylor, Jude Cogdon.
