Former Heerenveen coach Van Basten replaced Dick Advocaat during the close-season, but his future at the club is already in doubt amid reports in the Dutch media that he is to step down due to health issues which have led to him taking extended leave.
The former Netherlands striker is due to return to work Monday, but it remains to be seen whether the 49-year-old will stay on in the role as he is said to be have been suffering from heart palpitations since the death of his father in July.
Van Basten was again absent as Daley Sinkgraven scored the only goal of Saturday's Eredivisie clash 38 minutes in, pouncing on a ricochet to tuck the ball inside the right-hand post.
Supporters gave a round of applause for Van Basten in the 88th minute, but it failed to inspire AZ to snatch a point as Heerenveen saw out the win and moved on to 10 points, while the home side suffered a second league defeat.
Leaders PSV's imperious start to the season halted with a whimper as they were beaten 3-1 at PEC Zwolle, who moved level with them on 12 points.
Luuk de Jong netted from the penalty spot with 32 minutes gone to put PSV in front, but Zwolle battled back and were level just before the break as Jeroen Zoet inexplicably failed to keep out a Jesper Drost attempt.
Joost Broerse edged Zwolle ahead in the 65th minute with a delightful free-kick and Ben Rienstra added the third in the latter stages, clipping an audacious effort over Zoet and in off the crossbar as PSV's 100 per cent start to the season came to an end.
Ajax bounced back from two consecutive league defeats by beating Heracles 2-1 at home.
Arek Milik made the most of his chance to stake a claim for a regular spot as he filled in for the rested Kolbein Sigthorson and scored both goals.
His first arrived less than two minutes into the match, holding off the attentions of a defender before rifling across goal and into the bottom-right corner.
The forward's second arrived on the stroke of half-time, cutting in from the right and firing into the bottom-left corner and although Wout Weghorst pulled one back late on, Ajax did just enough to secure all three points.
Feyenoord's unimpressive start to life without Ronald Koeman continued as they lost 2-1 at home to Willem II, with Colin Kazim-Richards' 75th-minute debut goal not enough to earn a share of the spoils.
Twente recorded their first win of the season, ending a run of four consecutive league draws by beating Go Ahead Eagles 2-1.
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