Thorsten Fink's side had a chance to take three points, but were forced to settle for one after the Croatian forward drew die Roten level by striking against his former club
The Bavarians overcame an early deficit, but in a hard-fought second half, were unable to score a winner as the hosts held firm in defence.
Jacopo Sala stunned the visitors with a 23rd-minute goal, and HSV defended extremely well. However, Hamburg ultimately had their lead erased by their former striker, Ivica Olic, who found the net with 19 minutes left to play.
The hosts started the match in sublime form, and Mladen Petric and Heiko Westermann had good chances from set plays, but the Croat missed over the bar before the latter had his attempt cleared off the line by Toni Kroos.
Bayern were first to find the net, but Jerome Boateng's header was called back due to a push by Mario Gomez. The disallowed goal came moments after Jaroslav Drobny did very well to push Franck Ribery's low drive around the post for a corner.
The visitors again came close as Gomez did well to muscle Slobodan Rajkovic away from the ball before the Serb made a last-ditch challenge to deflect his shot over the bar.
After a scintillating start to the match, HSV were first to strike as Jose Paolo Guerrero delivered the ball to Sala, who volleyed into the net with his first touch.
The goal seemed to inject impetus in the Bayern team, but Rajkovic, Westermann, and the rest of the Hamburg defence held strong and greatly limited their visitors' opportunities: a long-ranged effort from Arjen Robben that was tipped over the bar was the only half-chance die Roten managed to create.
The second half provided more of the same, and Jupp Heynckes was forced to make attacking substitutions to erase the deficit. Ivica Olic came in to replace Toni Kroos on 64 minutes, and it was the former HSV man who restored parity on 71 minutes after Thomas Muller had an attempt denied by a stunning save. Following the resulting corner kick, HSV failed to clear the ball and Olic pounced on his opportunity to tap home from close range.
The game stretched in the closing stages, and both sides had chances to win. Robben and Bastian Schweinsteiger missed narrowly wide with long-ranged attempts, while at the other end, substitute Heung-Min Son latched onto a through pass and rounded Manuel Neuer before missing an open net.
In the end, the two sides had to settle for a draw, leaving Bayern two points behind leaders Borussia Dortmund, but level with Schalke, who are third on goal difference. Hamburg remain 11th, but are not equal with Stuttgart and just a point behind Wolfsburg and Hoffenheim.