After being wasteful for most of the game, the visitors finally found the net in the 89th minute, as Young pounced on a huge error by Tim Krul, meaning United are in the driving seat for fourth in the Premier League.
However, Newcastle should have been given the opportunity to take an early lead when Chris Smalling clumsily brought down Emmanuel Riviere, who caused the away side problems, but referee Anthony Taylor ignored shouts for a penalty.
United dictated proceedings for long periods before the break, although the first half was marred by an incident that seemed to show Jonny Evans and Papiss Cisse spitting at each other.
The second half produced a far more positive talking point, however, when Jonas Gutierrez made his long-awaited return from cancer, as Newcastle caretaker manager John Carver looked to counter the visitors' dominance with work rate.
But the match ultimately ended in disappointment for Newcastle, as Young steered home from close range just before the finish, giving United all three points in trademark fashion.
Despite being hauled off halfway through United's 2-0 win over Sunderland on Saturday, Angel di Maria retained his place in the starting line-up, with Marouane Fellaini replacing the dropped Radamel Falcao as Van Gaal's only change.
And the Argentinian put United into trouble after just eight minutes, as Gabriel Obertan cut out his cross-field pass and fed Riviere, who blazed over from the edge of the area.
The visitors enjoyed much of the early possession, although Newcastle should have been given a penalty in the 10th minute, Smalling escaping unpunished following a blatant trip on Riviere.
Newcastle were then lucky to remain level 16 minutes later, as Young knocked Di Maria's cross into the area for Wayne Rooney, who brought the ball down on his chest and stabbed wide from about 12 yards.
With the first half drawing to a close, Evans and Cisse appeared to spit at each other following a collision, before Krul palmed away a Fellaini header on the stroke of half-time.
Proceedings became considerably more frantic in the second half and both sides saw glorious chances go begging.
Newcastle were the first to go close in the 49th minute and they found United goalkeeper David de Gea at his best, as the Spaniard denied Riviere from point-blank range.
Krul was forced to match his counterpart a few moments later, rushing out to thwart Fellaini and then also blocking Young's effort from the rebound.
Carver introduced Gutierrez for Ryan Taylor with 25 minutes left and his entrance initially boosted Newcastle, who almost instantly crafted a fine chance, Cisse inexplicably missing the target after being fed by Ayoze Perez.
And United capitalised on that let-off with just a minute to go, as Krul panicked and played his clearance straight to Young, who coolly slotted into the bottom-left corner to secure a dramatic late win for the visitors.
'David Beckham was desperate to play in my squad, but I didn't want to bring him along and waste the FA’s money: I had to pick the strongest players': Great Britain coach reflects on Becks snub as 'one of the toughest decisions' of his career
Manchester City report: Bruno Guimaraes and Pep Guardiola discussions revealed, as rumours swirl he could replace Rodri
