Bayern Munich head to Qatar for the FIFA Club World Cup with a 10-point lead at the top of the Bundesliga after victory in snowy Berlin.
Bayern were dominant if not at their fluent best throughout, with Robert Lewandowski missing an early penalty.
Kingsley Coman scored the only goal with a deflected shot from range that looped over Rune Jarstein and in.
The German champions could not find a second goal and had a scare when Matheus Cunha ran clear but shot wide.
Hertha are only out of the relegation zone on goal difference.
Bayern will face Egypt's Al Ahly in the semifinals of the CWC as they look to win their sixth trophy in less than 10 months and match Barcelona's tally from 2009.
"It will now be a good flight," Bayern coach Hansi Flick said. "We wanted to leave for Qatar with a win."
"It was at times difficult and we had to overcome some phases where we did not have possession. But we defended our 1-0 lead at the end and so I am satisfied."
Champions League winners Bayern could win their sixth trophy in nine months if they win in Qatar.
Hertha had a golden chance to equalise a minute from the end when Matheus Cunha chipped the ball over keeper Manuel Neuer, but his effort rolled just wide of the goal.
Bayern are now on 48 points, while second-placed RB Leipzig, who travel to bottom side Schalke 04 on Saturday, have 38. Hertha are in 15th place on 17 points.