In a game short of clear-cut chances, United's best opportunity arrived during the first half, when Mason Greenwood's close-range attempt was well blocked. Jesse Lingard went close in the final 10 minutes, but a point was an appropriate result in a tight contest between two well-matched teams.
AZ themselves had several impressive efforts, but David De Gea straightforwardly repelled all those on target, as the Reds kept a first clean sheet for 11 away matches.
It leaves United tied on points at the top of Group L with Partizan Belgrade, who earned an away win in Kazakhstan earlier in the day by beating FC Astana 2-1.