The visitors took the lead through midfielder Cesc Fabregas in the 36th minute after he was found by Dutch international Robin van Persie and then comfortably soaked up the pressure.
But Alkmaar went on the offensive in the last 20 minutes and were finally rewarded when Mendes da Silva salvaged a point after Graziano Pelle set him up following a Stijn Schaars pass.
Arsenal remain top of the group with seven points, while Alkmaar have moved into third with two points.
"The late equaliser feels great as we know exactly how it feels to concede a late one," AZ coach Ronald Koeman said in reference to his side's previous match against Standard Liege when the Belgian side levelled in stoppage time.
Arsenal allowed their Dutch opponents to enjoy the majority of possession but the Premier League side carried the more potent attacking threat with AZ keeper Sergio Romero making several good saves.
"It was our mistakes that caused Arsenal's chances and the opening goal," Koeman added.
"They were controlling the match but did not have many chances."
Arsenal manager Arsene Wenger was left to rue his side's lack of killer instinct in front of goal.
"In bigger parts of the game we were superior and in control but as long you don't score a second goal you know they always can find their way back into the match," Wenger told reporters.
"I felt that they could only score with a set piece situation and that is what happened."
