Manager Jose Mourinho made four changes to the side against Fulham after their draw with Arsenal in midweek.
Young's first United goals since May 2016 were followed by an Anthony Martial strike as United produced a scintillating first half at Vicarage Road.
Zlatan Ibrahimovic's introduction as a second-half substitute proved crucial as Manchester United finally discovered a way to beat newly-promoted Brighton and Hove Albion.
Goals from Wayne Rooney, 18-year-old Marcus Rashford and substitute Ashley Young secured the three points, which was enough to lift Manchester United above Southampton into fifth place in the Premier League
Manchester United are a point behind second-placed Arsenal, who have played one match fewer, but Young is confident Louis van Gaal's third placed side can overtake the Gunners and finish as runners-up behind likely champions Chelsea.
Manchester United F.C. hit back through Ashley Young, Marouane Fellaini, Juan Mata and Chris Smalling to register a sixth successive league win after Sergio Aguero gave Manchester City F.C. an eighth-minute lead at a blustery Old Trafford.
Ashley Young's 89th minute goal secured three vital points at St James' Park on Wednesday for a relieved Louis van Gaal. Manchester United have lost only twice in their last 22 Premier League matches.
Louis van Gaal's team looked set to lose ground on their rivals in the race for the top four places until Newcastle goalkeeper Tim Krul gifted Young his first goal in 14 months with just a minute to go at St James' Park.
Manager Louis van Gaal is a disappointed man this New Year as he had to deal with injury problems after Manchester United's drawn EPL match against Stoke City.
Last Saturday's 2-1 win at Arsenal means Manchester United have now lost just one of their last seven games following the club's worst start to a season since 1986. For the first time this season, United are among the Premier League's Champions League qualification places.
The victory sends Manchester United into Monday's final of the International Champions Cup, a series of friendlies involving eight European clubs all preparing for their domestic campaigns.
Ashley Young hurt his shoulder in a collision with Tottenham goalkeeper Hugo Lloris that Moyes insisted should have led to a penalty for his side.
James Chester of Hull City turned from hero to villain for the hosts as he scored the opening goal in the fourth minute only to head one in for Manchester United in the 66th minute as well.
Ashley Young has not played a league game for Manchester United since they were thrashed 4-1 by bitter rivals Manchester City in September.
Young was booked for deliberately initiating contact with Crystal Palace midfielder Kagisho Dikgacoi in a failed bid to win a penalty in Saturday's 2-0 victory at Old Trafford.
Young for booked for diving during Manchester United's 2-0 victory against Crystal Palace.
Rejected by Liverpool as a youngster and then released by Blackpool in 2000 aged 18, Rickie Lambert was forced to work in a factory putting lids on jars of beetroot while he tried to keep his football career alive by training with minnows Macclesfield.
Wayne Rooney showed plenty of signs of rust in an erratic display, but his shoulder didn't look to be troubling him and Moyes, working as a television pundit, said he was happy to see the striker back in action.