Half-chances before the break for youngsters Mason Greenwood and Angel Gomes were the best Ole Gunnar Solskjaer's men could muster as their high-flying Eredivisie opponents brought most of the attacking creativity to the contest.
Playing on the artificial pitch of the Hague's Cars Jeans Stadion due to roof damage their AFAS Stadion in Alkmaar, AZ were unfortunate to find David de Gea in assured form.
United should have had a late chance to steal victory when referee Gediminas Mazeika waved away a strong penalty appeal from Marcus Rashford, but the stalemate remained intact.
Myron Boadu headed home Fredrik Midtsjo's 11th-minute cross but was correctly flagged offside before David de Gea sharply kept out Oussama Idrissi's drive.
It amounted to a familiarly listless opening from Solskjaer's men, although they almost led as the half hour approached when veteran defender Ron Vlaar made a vital block to deny Greenwood from Daniel James' cutback.
Diogo Dalot lost Boadu in the 32nd minute, with the AZ striker unable to contort himself and head effectively goalwards.
There was better work from Dalot shortly afterwards when Gomes' shot from his teasing right-wing cross was blocked.
AZ resumed on the front foot, firing balls into the United box and seeing a couple of penalty shouts against Dalot and full debutant Brandon Williams waved away.
Solskjaer introduced Rashford for James after the hour but the hosts continued to look most likely to breakthrough as De Gea pawed away a swerving Owen Wijndal drive.
Idrissi fizzed a half-volley narrowly wide from Boadu's lay-off and saw De Gea fist a powerful 77th-minute shot to safety.
The lack of VAR spared Stijn Wuytens when he clumsily challenged Rashford, while fellow substitute Jesse Lingard endured a painful end to the game the day he was dropped by England – lashing a good chance wide before pulling up with an apparent hamstring injury.
What does it mean? Same old story for United
Solskjaer's commitment to giving youth its head is admirable but whatever configuration he throws out, United simply do not score enough goals or look like doing so. Since the rousing 3-1 victory at Paris Saint-Germain that sealed the job on a full-time basis for the Old Trafford hero, his side have neither won nor scored more than once in any away game. They failed to register a single effort on target here.
Manchester United's number one has seen his once peerless reputation take a battering over the past year, with a series of high-profile mistakes staining his body of work. But in difficult conditions operating behind a confidence-shorn team, De Gea's handling was sure and his shot-stopping sharp. United would have lost without him.
Dread the Fred
When it starts to feel surreal that United have such a thin, uneven and flawed squad despite spending so much money, you can remind yourself Fred cost £52million. The artificial playing surface hindered both sides to an extent. The Brazilian midfielder sometimes looked like he was trying to pass a football on the surface of the moon.
United must try and win a first Premier League away game since February when they travel to struggling Newcastle United on Sunday, when AZ will pursue a fifth consecutive Eredivisie victory at Willem II.