Mo Sedibeh, making his competitive debut at under-21 level, opened the scoring at Whitley Park, stroking the ball home from Darren Palmer's cross, before Charlie McArthur's own goal levelled the last-eight tie before the half-time break.
United's youngsters, however, netted twice in the space of five second-half minutes, with Sedibeh's composed finish restoring the hosts' lead before Alfie Harrison's strike, his first goal at under-21 level, doubled Newcastle's advantage.
Josh Donaldson's close-range rebound added gloss to the scoreline before Johnny Emerson's stoppage-time finish rounded off the scoring as Diarmuid O'Carroll's side secured their spot in the last-four, maintaining their hopes of lifting the trophy for a 41st time.
United's youngsters, who won the competition last season following a 2-1 win against Blyth Town in the final at St. James' Park, began the contest in strong fashion as Sedibeh went close to netting inside two minutes of his maiden outing for Newcastle's second-string, darting inside from the left flank before his low strike flashed wide of the left-hand post.
Donaldson hit the post for the hosts moment later as the Gateshead-born striker connected with Dylan Charlton's low cross but the 18-year-old's first-time effort from close range struck the woodwork.
United goalkeeper Aidan Harris, who was named on the bench for the Magpies' UEFA Champions League away clash against AC Milan in September 2023, was forced into action shortly after as the teenage shot-stopper held Yannick Aziakona's curling long-range strike.
In the 19th minute, Newcastle took the lead through Sedibeh as the Spanish forward, who arrived at St. James' Park last summer following his departure from Bradford City, latched onto Palmer's low cross before drilling a first-time effort past Alnwick goalkeeper Matthew Alexander.
Despite dominating large spells of possession, United's youngsters were dealt a frustrating blow as Alnwick equalised through McArthur's own goal as Luke Baston's cross from the right wing was hooked across the penalty area before the ball inadvertently struck the teenage centre-back's leg before trickling into the bottom right-hand corner.
In the second-half, Harris produced an important stop to prevent Usman Ogidan sending the visitors ahead, standing tall to block the Wick striker's shot inside the penalty area, who had raced through on goal.
In the 57th minute, Sedibeh netted his second of the evening as the 18-year-old latched onto a lofted through pass before calmly rolling the ball underneath Alexander.
Harrison, introduced from the bench at the restart, doubled Newcastle's lead in the 62nd minute as the attacking midfielder, who joined the Magpies from Manchester City in February 2024, fired a close-range effort into the net.
Donaldson netted his second goal in as many games at second-string level in the 69th minute. After Ellis Stanton's low drive from the edge of the box was spilled by Alexander, the 19-year-old was quickly on hand to fire a close-range rebound into the roof of the net.
Emerson, another substitute, got his name on the scoresheet as the Carlisle-born winger, a representative of Scotland at under-19 level, scored United's fifth of the night after beating Alexander to a loose ball and, after knocking the ball around the Town goalkeeper, slotted the ball into an empty net.
Newcastle United Under-21s: Aidan Harris, Harry Powell, Rory Powell, Charlie McArthur (c), Dylan Charlton (Cathal Heffernan 82), Ellis Stanton, James Huntley, Scott Bailey (Alfie Harrison 46), Darren Palmer, Mo Sedibeh (Johnny Emerson 82), Josh Donaldson.
Substitutes: Adam Harrison, Anthony Munda.
