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.