John van den Brom's side needed 41 minutes before they were able to open the scoring at the AFAS Stadion; Steven Berghuis' sixth goal of the campaign giving the hosts the lead.
A nervy second half followed, although Dabney dos Santos eased the pressure with a goal in stoppage time, lifting AZ into third.
Davy Propper helped lift Vitesse above PEC Zwolle with the decisive goal in their clash at the GelreDome, the young striker lifting the ball over Warner Hahn four minutes after the hour to seal a 2-1 win.
Mustafa Saymak had given the visitors a good start with a diving header inside the fifth minute, only for Bertrand Traore to level things up after 34 minutes.
Vitesse could have gone into the break ahead with a late penalty but Marko Vejinovic blazed over from 12 yards, leaving Propper to be their match winner.
Twente thought they had ended a four-match losing run against NAC Breda thanks to Luc Castaignos' early goal but Erik Falkenburg snatched a point for the visitors with two minutes to play.
The 1-1 draw moved NAC closer to safety at the bottom, while piling the pressure on Twente boss Alfred Schreuder.
Meanwhile, Sander van de Streek's sixth goal of the campaign was enough to give Cambuur a ninth league win, the 21-year-old's 19th minute strike enough to earn a 1-0 victory over Heracles.
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