Ali Elkhattabi grabbed the opening goal for AZ on 18 minutes and when he netted again with seven minutes left, the hosts appeared to be comfortably poised for the spoils.
But within 60 seconds, Glen Salmon reduced the arrears for Groningen only for AZ to hang on grimly in the closing stages.
Heerenveen ensured ADO Den Haag remain entrenched in the relegation zone after a comfortable 2-0 home success.
Former Sheffield Wednesday striker Gerald Sibon opened the scoring on 33 minutes and Georgios Samaras wrapped up the win with ten minutes remaining.
Volendam boosted their survival prospects with a 2-0 triumph over Twente Enschede - courtesy of a goal in each half from Dion Esajas.
Click below for an individual match summary:
AZ Alkmaar 2-1 Groningen
FC Volendam 2-0 Twente Enschede
Heerenveen 2-0 ADO Den Haag
Click here for an updated Eredivisie table.
