Teed up by Thomas Muller, the Dutchman curled in from 20 yards out with 21 minutes gone and Pep Guardiola's men survived a few late scares to claim all three points
Bayern have fond recent memories of the Olympiastadion, having sealed the Bundesliga title there last March before beating Borussia Dortmund in the DFB-Pokal final three months later, and Pep Guardiola's team looked very much at home right from the off on Saturday.
A typically dominant first-half display was illuminated by Robben's wonderful goal shortly before the half-hour mark and, in truth, the champions - showing few ill-effects from their 3-2 Champions League defeat at Manchester City in midweek - should have gone in at the break two or three to the good.
Hertha hung on and contributed to a much more even contest in the second period as Bayern's intensity dropped, but they were unable to find a way past Manuel Neuer - who kept a clean sheet for the 10th time in 11 Bundesliga outings.
Robben's strike was sufficient to ensure what appears to be another Bayern procession to the title rolls on, with Guardiola's side now 10 points clear of Wolfsburg ahead of their meeting with third-placed Borussia Monchengladbach on Sunday.
Guardiola recalled Dante, Mario Gotze and Thomas Muller to his starting line-up after they were rested for the game in Manchester, and it was the latter of that trio who created Bayern's first chance after just two minutes.
Muller raced away down the right and fired in a superb low cross, which an under-pressure Robert Lewandowski could only put well over the bar from six yards.
Predictably, Bayern dominated possession, with the fluid interchanging between Muller, Lewandowski, Franck Ribery and Robben causing Hertha no end of problems.
And it was three of that foursome who combined brilliantly to give the champions a deserved lead 27 minutes in.
The elusive Ribery popped a ball into Gotze, before Muller deftly flicked the ball into Robben's path and the Dutchman curled an unstoppable left-footed effort beyond Thomas Kraft from 25 yards.
Hertha were struggling to get out of their half and Robben almost doubled his tally shortly before the break when he diverted Lewandowski's pass off target.
To their credit, Hertha attempted to get a foothold in the game early in the second half, Julian Schieber had their first shot on goal three minutes after the restart, but the former Dortmund striker sliced wide from an acute angle.
Bayern were less vibrant after the interval, but the scare of Hajime Hosogai having a goal correctly ruled out for offside seemed to spark the Bavarians back into life.
Lewandowski had a good chance to seal the points on 72 minutes when he latched on to Robben's pass, but the Pole scuffed wide of Kraft's far post.
It was simply not Lewandowski’s day in front of goal, as Kraft made an excellent stop to deny him shortly after, but the ex-Dortmund man’s profligacy mattered little as Bayern racked up their 10th league win of the season despite some late Hertha pressure.