Arjen Robben and Robert Lewandowski were both at the double before Franck Ribery rounded out the scoring as Bayern sealed their progression to the Champions League round of 16.
The Bavarians remain unbeaten through five games in Europe but have found life much tougher on the domestic front this season, sitting fifth in the league and nine points back of league leaders Borussia Dortmund.
Their struggles in the Bundesliga have left Kovac on the hot-seat, but star man Robben was happy to see the team perform up to potential as he believes Kovac "belongs" to the players.
"I was especially looking forward to our coach today." the winger told reporters after the club advanced from the group stage. "As a person, he has earned it. He belongs to us."
Despite the win, the Dutch star knows that one game does not make for a turnaround and that the club will have to continue to perform at a high level to save Kovac's job.
"We have to see that," the winger said when asked if the win would change the outlook for the team. "That's just a game. If you do not win Saturday, it will be trouble again."
The winger also played down reports of unrest in the dressing room, saying: "Nothing happened in the locker room. The atmosphere in the team is good. You win together and you lose together."
Goalkeeper Manuel Neuer backed the manager and wants to see everybody at the club pulling in the same direction.
"Of course, the team plays for the coach," he said.
"We have a huge responsibility, because we are the protagonists on the pitch. We are all in a boat together."
Tuesday's win was just the second in the last five matches for Bayern across all competitions, with the club having lost to Borussia Dortmund and dropped points against both Freiburg and Fortuna Dusseldorf.
Despite their struggles, sporting director Hasan Salihamidzic was pleased with Tuesday's showing.
"That was a victory of Bayern Munich," he said. "The boys played for themselves, for Bayern, for the coach. That was very, very good today.
"We said that we will talk after the game and the conversation will certainly be very pleasant."
The 41-year-old also said the club have not started thinking about changing managers.
"No we have not," he responded when asked if they had started the search for a new boss. "We did not think about whether we would hire another coach."