The visitors went two up in Alkmaar before an own goal from Tjaronn Chery and Gudelj, who had earlier missed a penalty, completed a second-half comeback.
Michael de Leeuw scored for the fifth time in five starts this season to put Groningen ahead on 10 minutes.
Eric Botteghin's foul inside the box on 57 minutes provided Gudelj with the chance to reduce the deficit. He missed the penalty, but Groningen defender Chery bundled the ball into his own net in the scramble that followed.
Groningen would have climbed to fifth in the table with victory and were ahead until the 82nd minute, when Gudelj made amends for his poor spot kick by popping up at a set piece to salvage AZ a point.
The result means that AZ remain ninth, while Groningen are one place below them and level on points.