Bert van Marwijk's men had won just once at home in the Bundesliga all season going into the game and that run looked set to be extended when Alexandru Maxim put Stuttgart ahead within three minutes.
However, Hertha Berlin loanee Pierre-Michel Lasogga levelled the scores19 minutes later, only for Christian Gentner to head the visitors back in front prior the break.
After the interval, the goals continued to flow with Hamburg substitute Maximilian Beister equalising for a second time before Johan Djourou's own goal put Stuttgart back on top.
However, Rafael van der Vaart proved Hamburg's hero, securing a point for his side after 67 minutes finishing Beister's pass.
Luiz Gustavo's first goal for Wolfsburg sealed a 2-1 win over Augsburg, although Dieter Hecking's side had to come from behind to win.
Coincidentally, the goal was his first in the league since Bayern beat Augsburg 3-0 in May.
