Last weekend's 5-1 humbling at the hands of Eintracht Frankfurt was only Bayern's second defeat of the season but turned out to be more than enough for the board to pull the trigger on Kovac, who never managed to properly impose his style in Bavaria.
The result has left Bayern, normally cruising at the top, marooned in fourth place and four points behind surprise leaders Borussia Monchengladbach after 10 Bundesliga games.
While the situation is far from dire, Bayern players will know that they must combine their attacking potential with an element of collective grit if they are to reign supreme in Germany and Europe like the Jupp Heynckes team that reached consecutive Champions League finals in 2012 and 2013.
On current evidence, however, Bayern's ability to control games has somewhat diminished this season, with Arjen Robben and Franck Ribery's departure over the summer leaving behind a talented but perhaps more inexperienced group of players.
The meeting with Lucien Favre's side, who will look to hit the German champions hard on the counter, should serve as a strong indication of how much mettle this Bayern team can exhibit when the heat is really on.
In Dortmund's last four visits to the Allianz Arena, they have been on the wrong end of an aggregate score of 20-2, losing 5-0, 6-0, 4-1 and 5-1 respectively since October 2015.
For a team that usually serves as Bayern's chief source of domestic competition, such a horrible record comes as a surprise, but it can also be partly explained by a historical inferiority complex towards its more successful, richer rival, much like how Marseille views Paris Saint-Germain or how Napoli views Juventus.
However, Dortmund have good reason to believe that this year's visit to Bavaria could be different, with Bayern lacking its usual inner sense of arrogance at a time when they are managed by assistant coach Hansi Flick.
While one club finds itself undergoing notable change, Dortmund are motoring along under the guidance of Favre, whose side has the joint best defensive record in the league this season and also boasts prodigal young attacking talents such as Julian Brandt, Thorgan Hazard and Jadon Sancho.
Indeed, with just one point separating the two teams in the Bundesliga, perhaps the key variable on Saturday will be how well these Dortmund players can compose themselves in the cauldron of the Allianz Arena.
Recent Bayern Munich form: DWWWLW
Recent Borussia Dortmund form: WLDWWW
Bayern are definitely without Niklas Sule for this game after the defender suffered a serious knee injury that has ruled him out for the season.
Favre faces an anxious wait on the fitness of Sancho, who picked up a hamstring strain during the week, and will also make a late call on Hazard and Marco Reus ahead of the game.
Bayern Munich possible starting lineup:
Neuer; Pavard, Martinez, Alaba, Davies; Kimmich, Thiago; Coutinho, Gnabry, Coman; Lewandowski
Borussia Dortmund possible starting lineup:
Burki; Piszczek, Akanji, Hummels, Guerreiro; Witsel, Weigl; Hakimi, Brandt, Sancho; Gotze
We say: Bayern Munich 2-2 Borussia Dortmund
Dortmund come into this game in excellent shape having won three games on the bounce but will be conscious of how quickly things can go wrong against Bayern in their own stadium.
Expect a furiously-paced affair, with both sides looking to score through sharp counter-attacking movements up the pitch. We get the sense that this game will either end in a draw or with one team suffering a heavy defeat.
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