The reigning champions headed into a crunch Der Klassiker clash with old adversaries on Saturday sat second in the standings.
A 5-0 win later and they are back at the summit and looking to push on towards a seventh successive German top-flight crown.
Success in his debut campaign would help Kovac to answer some of the questions that have been asked of him this season.
Karl-Heinz Rummenigge concedes that Kovac cannot afford to take his position for granted, with everybody at the Allianz Arena under expected to deliver or accept the consequences.
Bayern’s CEO said of the current manager at the helm: "There is no job guarantee for anyone at FC Bayern Munich.
"You always have to deliver at FC Bayern Munich.
"That's how FC Bayern Munich function and you must cope with this pressure. If you can't do it, you are at the wrong club."
Rummenigge is preparing to make his own departure from Bayern.
"The concrete plan is that Kahn will become my successor," Rummenigge said.
"My contract expires in December 2021. I am convinced he'll be a good successor."
It remains to be seen whether Kovac is still in the dugout at that point.
He has been around long enough to know that Rummenigge’s warning applies to any coach, at any club.
If he fails to live up to expectations, then he will be moved on.
There are, however, no immediate plans for another change in Bavaria, with Bayern president Uli Hoeness responding to Rummenigge’s comments by offering his support to Kovac.
He said in Kicker: "It would not even be a disaster if were to win finish second."