Groningen will have home advantage in Sunday's return leg as both sides were left to rue missed chances at the AFAS Stadion.
AZ controlled the early exchanges but that momentum slowly began to wane and Groningen were unlucky not to take a lead into the break.
Johann Gudmundsson wasted the hosts' best chance when he blasted over the bar from the edge of the penalty area, and Tjaronn Chery nearly punished him with a well-taken free-kick that went just wide.
Chery again went close at the start of the second half but Esteban Alvarado was equal to it in the AZ goal, and with time running out substitute Aron Johannsson wasted an effort to give Dick Advocaat's men an advantage.
In the battle to earn a place in the top flight next season the only Eredivisie side left suffered a surprise shock.
RKC Waalwijk were behind early on against Excelsior as Khalid Karami gave the second division side the lead in the second minute, and when Lars Veldwijk doubled their advantage from the penalty spot just before half-time things looked bleak.
Try as they might Waalwijk were unable to get back into the game and will need a heroic performance in the second leg to preserve their top-flight status.
Meanwhile, Dordrecht will be happier with their 2-2 draw against Sparta Rotterdam thanks to their two away goals, even though Sparta twice came from behind to restore parity.
