AZ, who fired coach Gertjan Verbeek just over a month ago and replaced him with ex-Netherlands boss Dick Advocaat, beat struggling Den Haag with a workmanlike performance to reach 22 points, one more than Vitesse who snatched a late win at Ajax.
Twente Enschede slipped from top spot to third after a 2-2 home draw with bottom side NEC Nijmegen left them on 20 points, while PSV have 19 after a 1-1 draw with visiting PEC Zwolle cast more doubt on their title credentials after a promising start.
The second goal from the Icelandic international was a spectacular effort from 30 metres.
Substitute Valeri Qazaishvili stole possession in the 89th minute to score for Vitesse as they stunned Ajax away for a second successive season to move into second spot while Ajax slipped three places to fifth on 19 points.
"Vitesse took advantage of our mistakes," Ajax coach Frank de Boer told reporters as he now turns his focus to a Champions League game at home to Celtic on Wednesday
Twente, who have clung precariously to the leadership over the last weeks, have now gone three league games without a win after squandering a two-goal lead over NEC.
Goals by Shadrach Eghan and Quincy Promes put Twente ahead at halftime but Soren Rieks and Austrian import Jakob Jantscher scored early in the second half to bring the scores level.
PSV's draw in stormy conditions against Zwolle, who are sixth also on 19 points, is further evidence of a slump by the former European champions after a surprise midweek cup exit and an internal report that criticised club management.
PSV took the lead through Jeffrey Bruma in the second minute but PEC levelled 11 minutes later thanks to Ghanaian striker Fred Benson, who was sent off five minutes from time.