Klaas-Jan Huntelaar gave the home side the lead in the second minute, but a Rafael van der Vaart penalty brought Hamburg level 10 minutes later.
An own goal from Timo Hildebrand gave Hamburg the lead in the 24th minute, but Huntelaar's second of the game on the stroke of half time brough the Royal Blues back on terms.
Lasse Sobiech put Hamburg in front for the second time early in the second half, but Adam Szalai salvaged Schalke a point in an entertaining encounter.
Schalke made the best possible of starts when Julian Draxler played a ball into the path of Huntelaar and he picked his spot low into the bottom left-hand corner of Rene Adler's goal.
The lead lasted just 10 minutes before Van der Vaart equalised from the penalty spot after Joel Matip handled Marcell Jansen's cross inside the penalty area.
Schalke lost Draxler to inury in the 22nd minute, and just two minutes later, things took another turn for the worse when Hamburg took the lead.
A sweeping Heiko Westermann ball picked out Dennis Diekmeier in an advanced position down the right and his cross was headed against the bar by Maximilian Beister.
The ball bounced back into play, but ricocheted off the back of Hildebrand to cross the line.
The injury to Draxler meant two minutes of stoppage time were played at the end of the first half, and Schalke took full advantage, levelling with the last touch of the half.
Huntelaar was left an inexplicable amount of room to head Christian Fuchs' cross in from five yards out for his second goal on the day before his 30th birthday.
Hamburg regained the lead early in the second half when Sobiech's header struck the underside of the bar without any need for Hildebrand to help it over the line this time.
Schalke's response was to send Szalai on for Roman Neustadter and he made an instant impression.
The Hungarian brought a fine reflex save out of Adler in the 69th minute before marking his Schalke debut with a goal two minutes later.
This time, Adler was guilty of a glaring mistake as he fumbled Christian Clemens' shot to the feet of Szalai, who tucked the ball into the bottom corner from close range to clinch a draw.