Italian Jacopo Sala fired the hosts into a 23rd minute lead, thundering in a volley from a pinpoint Paolo Guerrero cross.
Put under pressure deep in their own half, Bayern had constant problems implementing their game plan and had to wait until the 71st minute to level with former Hamburg player Olic scoring from close range seven minutes after coming on.
"It was very difficult for us because Hamburg ran a lot and were constantly pressing," Olic told reporters. "They scored and then waited for quick breaks but we put pressure on them and got our chance. It's better to have a point than not."
"I can't blame the team," said Bayern coach Jupp Heynckes, whose side are chasing a treble of German league and Cup titles and the Champions League.
"We played well but the demands of playing at Bayern are higher and so we cannot really be satisfied," said Heynckes.
VfB Stuttgart rescued a 2-2 draw at 10-man Bayer Leverkusen thanks to substitute Martin Harnik's close-range goal in the 89th minute as both teams finished with 10 men.
Bayer's Michal Kadlec was dismissed just past the hour mark and Stuttgart's Cristian Molinaro was sent off in added time.
It was Hertha's third straight defeat since Michael Skibbe took over and left them just two points above the drop zone.
