"It was a very crazy game," Maxim said.
Beister set up Van der Vaart to equalize for the third time three minutes later, ensuring fellow Dutchman Van Marwijk is undefeated after three games in charge, though Hamburg remains just one place above the relegation zone.
Stuttgart defender Antonio Ruediger was sent off late on for punching Van der Vaart in the stomach.
"We were jostling, I pushed back, he punched me. That was that," said Van der Vaart, who collapsed as if seriously wounded.
Wolfsburg came from behind to snatch a 2-1 win at Augsburg in the late game.
Tobias Werner gave the home side a deserved lead in the 10th, scoring from a rebound after Halil Altintop and Matthias Ostrzolek's initial efforts were saved by Diego Benaglio.
Werner should have scored again minutes later but miscued his shot with only the goalkeeper to beat from close range, and he missed another chance, as did Altintop, before Maximilian Arnold equalized with a long-range effort in the 35th.
"You could see there was uncertainty there for the first 20 minutes, but after that, the team showed what it can do," said Wolfsburg coach Dieter Hecking.
Luiz Gustavo was left unmarked to meet Ricardo Rodriguez' free kick for his first Wolfsburg goal in the 42nd. The Brazilian's last goal was also against Augsburg, in May, while playing for Bayern Munich.
Augsburg pushed hard for an equalizer in a gritty second half but the visitors held on for their first away win of the season.
"You need effectiveness in the Bundesliga. We didn't show it today and so deserved to lose," said Augsburg coach Markus Weinzierl.
