Goals from Cameron Jerome and Alex Tettey either side of half-time proved enough for the Canaries, despite a reply from Anthony Martial
United left the field to boos after failing to win for a sixth game in succession in a damaging run that has placed question marks over Van Gaal's future.
The result also made for a miserable afternoon for captain Wayne Rooney on the occasion of his 500th appearance for the club
The England linchpin started brightly but was unable to wrest back the initiative once the Canaries, who had been without a win at Old Trafford since 1989, took command with two breakaway goals
United controlled possession early on and showed plenty of attacking intent, with Rooney operating centrally, but they failed to test visiting goalkeeper Declan Rudd.
Rooney did poke the ball past Rudd in the 10th minute, but the flag had already been raised for offside against Marouane Fellaini.
Mephis Depay clipped an effort over the bar and Rooney dragged another shot wide before the pair combined to create another chance only for Russell Martin to clear.
After a long period on the back foot, Norwich eventually served warning of their ability on the counter-attack as Tettey beat Chris Smalling with a neat bit of skill only to shoot wide from distance.
The opening goal also came on the break as Nathan Redmond surged down the right and pushed the ball past the static Phil Jones to feed Jerome
The striker took up the charge and turned inside the diving Ashley Young before firing a fierce shot through the arms of David de Gea.
United fans' frustration was immediately evident, and even more so at the interval, although the boos turned to loud applause as the players reached the tunnel.
But worse was to follow after the restart as the Canaries doubled their lead with 54 minutes gone.
Rooney, perhaps in frustration, had ventured back into midfield to try to retrieve possession, but lost out and Jerome quickly released Tettey
The Norwegian was quickly into his stride and raced into the area before beating a helpless De Gea with a low shot into the corner.
United were jolted back into action and started to show greater urgency.
Rooney missed the target with an overhead kick before a Young cross created the chance for Martial to pull one back
The Frenchman got a lucky deflection off one defender, but then nimbly avoided Ryan Bennett and lashed a powerful drive into the roof of the net.
Fans responded with chants of "attack, attack" and more pressure and chances came, but United could not take advantage.
Rooney was unable to turn in a ball across the area and miscontrolled another pass, while Juan Mata had a free-kick pushed away by Rudd.
United had one last chance in the dying moments, but Smalling could not keep his header on target.
TWEET OF THE MATCH
Alex Shaw (?@AlexShawESPN) - " You have a choice of three: Mourinho, Ancelotti or Giggs
What in God's name are United doing if they even consider Giggs."
PLAYER RATINGS
MANCHESTER UNITED
David de Gea: 5
Ashley Young: 6
Phil Jones: 5
Chris Smalling: 5
Daley Blind: 6
Michael Carrick: 6
Maraouane Fellaini: 6
Juan Mata: 6
Memphis Depay: 7
Wayne Rooney: 7
Anthony Martial: 7
Substitutes:
Ander Herrera: 6
NORWICH
Declan Rudd: 6
Russell Martin: 7
Ryan Bennett: 7
Sebastien Bassong: 7
Martin Olsson: 7
Gary O'Neil: 6
Alex Tettey: 8
Nathan Redmond: 7
Wes Hoolahan: 6
Robbie Brady: 6
Cameron Jerome: 8
Substitutes:
Jonny Howson: 6
Dieumerci Mbokani: 6
Youssouf Mulumbu: 7
STAR MAN
Cameron Jerome
The Norwich striker had already given warning of his threat with a shot wide before he showed great composure to open the scoring
Jerome took up the attack after good work by Nathan Redmond and charged into the area before lashing the ball past David de Gea.
MOMENT OF THE MATCH
Referee Michael Oliver had an excellent game - one of those where he was hardly noticed
One moment did catch the eye, though
Midway through the first half Martial was fouled by Gary O'Neil but got up and attempted to play on
Oliver tried to allow advantage but when O'Neil won back the ball he immediately blew for the offence and booked the Norwich man
It was good refereeing.
VIEW FROM THE BENCH
This was not pleasant viewing for Louis van Gaal as his side, despite controlling long spells of the game, failed to create enough chances in front of goal to threaten a much-needed victory
United were not as rigid as they have been of late but the sharpness of attack was not there and confidence seems to be ebbing away
Confidence should not be a problem for Norwich after this well-disciplined win
Alex Neil's men initially had to sit back but they took their chances when they came and held firm to take the points.
MOAN OF THE MATCH
Norwich fans enjoyed their first win at Old Trafford in a quarter of a century, rubbing it in with chants of "Jose Mourinho - he's taking your job," aimed at Van Gaal and "Is this a library?" at the United supporters
United fans could not muster a response
It was as if they lacked the enthusiasm
That may be rubbing off on the players at a time when they could do with vocal backing.
WHO'S UP NEXT?
Stoke v Manchester United (Barclays Premier League, Saturday, December 26)
Tottenham v Norwich (Barclays Premier League, Saturday, December 26)
Source : PA
Source: PA