The draw means Bert van Marwijk remains unbeaten as coach of Hamburg, who sit three points above the relegation zone and six behind eighth-placed Stuttgart.
Stuttgart went in front through Alexandru Maxim after three minutes but Pierre-Michel Lasogga equalised in the 22nd minute when punishing a mistake from Stuttgart’s William Kvist.
However, Rafael van der Vaart quickly replied for Hamburg to ensure a point apiece, with Stuttgart having to survive a late red card shown to Antonio Ruediger for punching Van der Vaart.
"We were jostling, I pushed back, he punched me. That was that," said the Dutch playmaker.
Later in the evening, Wolfsburg showed similar resilience to come from a goal down to beat Augsburg 2-1.
Tobias Werner put Augsburg in front after 10 minutes but Maximilian Arnold equalised in the 35th minute and Luiz Gustavo claimed a rare winner before half-time.
Wolfsburg are now ninth in the table, with Augsburg in 13th.