The Eredivisie's bottom club had drawn twice prior to the winter break, but it was back to reality in Alkmaar as they suffered a 13th defeat of the season.
AZ enjoyed total domination from the first whistle as they boasted 62% possession and prevented their opponents from having a shot on target before the break.
They got the goal that their superiority warranted when former Fulham forward Muamer Tankovic delivered for Poulsen to convert on 25 minutes.
The home side were two up six minutes into the second half as Markus Henriksen picked out Gudelj to double their lead.
Dordrecht have not scored twice in a game since September and so the points were effectively sealed as AZ cruised through the remaining time.