Jacopo Sala's scored his first Bundesliga goal to put Hamburg in front on 23 minutes but former Hamburg striker Ivica Olic levelled with less than 20 minutes remaining to rescue a point for Bayern.
Schalke - who started the day in third - were held to a 1-1 draw by Mainz.Schalke had to come from behind to win their point at the Veltins Arena in Gelsenkirchen, with Egyptian forward Mohammed Zidan scoring the opener for Mainz after just 15 minutes.
Nigerian Chinedu Obasi levelled proceedings just before the hour mark but Huub Stevens' side were unable to find the elusive winner.
Moenchengladbach came away with a goalless stalemate at Wolfsburg.Moenchengladbach's unbeaten record extended to four matches with their draw, although they too failed to close the gap on Borussia Dortmund at the top of the league.
Both teams were struggling to create much in the way of goalmouth action, with the visitors edging the run of play during the first half.
Wolfsburg upped the tempo after the interval, but Marc Andre Ter Stegen still had precious little to do in the Gladbach goal in the second half as the match finished all square.
Elsewhere, a 10-man Stuttgart snatched a late point in an entertaining 2-2 draw at Bayer Leverkusen.
The hosts - who opened the scoring through Stefan Kiessling after just 11 minutes - also finished the match with 10 men at the BayArena.
Julian Schieber responded on 24 minutes for Stuttgart with a powerful free kick into the bottom corner that left Bernd Leno in the Leverkusen goal with no chance.
But a penalty from Simon Rolfes just after half-time looked to have given Leverkusen all three points.
Michal Kadlec's red card on 63 minutes put Leverkusen's hopes in doubt and the visitors made their numerical advantage pay in the dying stages as Austrian substitute Martin Harnik scored with just a minute of normal time remaining.
There was still enough time for Stuttgart's Italian defender Cristian Molinaro to be sent off although both sides were forced to share the spoils.
In other matches, Sebastian Langkamp's 72nd-minute equaliser helped relegation-threatened Augsburg to a 2-2 draw at mid-table Hoffenheim
While Norwegian Mohammed Abdellaoue scored the only goal in Hannover's 1-0 win at Hertha Berlin.
Freiburg will meet Werder Bremen, Kaiserslautern will against Cologne tomorrow.
