After a bright start from the Magpies at the University of Bolton Stadium, the Trotters opened the scoring through Matthew Argent-Barnes with a low strike beyond Dan Langley on the half-hour mark.
Eddie Brown doubled Wanderers' lead midway through the second half with a close range header before the Magpies pulled one back through Jack Young's excellent free kick.
Bolton punished the Magpies for their early missed opportunities in front of goal as Argent-Barnes sent the Whites into the lead.
After Wanderers pressured the United penalty area, the ball fell to the forward who smashed a low drive under Langley from a tight angle.
United almost got back on level terms before half-time as Kain Reed's powerful effort was palmed away by Callum James after Young's accurate ball into the forward.
In the second half, Langley produced a magnificent save to prevent Brown from doubling the home side's lead, clawing away a strong first-time header from ten yards out.
However, Brown managed to get on the scoresheet moments later after reacting quickest to Ronan Darcy's header, which was tipped onto the crossbar by Langley.
The Magpies kept fighting and Thomas Cole almost pulled one back after pouncing on a defensive mistake but the teenager's low driven strike was saved by James, as the Welsh youth international pushed his effort onto the woodwork.
United were given a lifeline in the tie after Young's delightful free kick. After a retaken set piece on the edge of the box, the 17-year-old fired his second attempt hard and low into the far corner.
The Magpies thought they had completed their comeback after another corner was powerfully headed towards goal by Jude Swailes.
After his first attempt was kept out by James, the defender thought his rebound had crossed the line, but the referee controversially decided otherwise after a group of Bolton bodies cleared the ball away from the goal line.
And, despite pushing for an equaliser, Dave Watson's side were unable to force the game into extra time as the Trotters advanced into round four.
Newcastle United Under-18s: Dan Langley, Ryan Barrett, Jude Swailes, Oisin McEntee, Max Allen, George Rounsfell, Sam Joyce, Jack Young, Joe White, Reed (Josh Harrison 74), Thomas Cole
Subs not used: Will Brown, Elliot Anderson, Lucas de Bolle, Tai Ebanks