Robert Lewandowski's astonishing run of goalscoring form continued with a brace as Flick's side built on their 2-0 Champions League win over Olympiakos.
Flick has steadied the ship following the departure of Niko Kovac, who was sacked after a 5-1 defeat at Eintracht Frankfurt last Sunday – the club's heaviest Bundesliga loss since April 2009.
Former long-serving Arsenal manager Arsene Wenger has been in the frame for the job, with suggestions he would take over until the end of the season.
Bayern's executive board chairman Karl-Heinz Rummenigge, though, suggested Flick would be remaining in his post for the time being.
"Hansi Flick has said that the two games against Olympiakos and Dortmund were his first finish line. Well, he has exceeded that brilliantly. Now we will calmly continue with him," Rummenigge said in quotes on the Bayern Munich official website.
"If you win such a game 4-0, of course you are very satisfied. The spectators had a lot of enjoyment with the game."
German broadcaster SPORT1 also quoted Rummenigge as suggesting he would call Wenger to "clear things up" surrounding their recent conversations.
Bayern president Uli Hoeness confirmed the club would take their time over any permanent appointment.
"You can see that Hansi Flick copes well with the team. He has always had a good relationship with the team as an assistant coach and the team has delivered," Hoeness said.
"These two games have helped the leadership have time to think about this topic in peace.
"I am convinced that there are no quick fixes and I think that the first person to talk to will be Hansi Flick for the next weeks."
Flick, meanwhile, is determined just to focus on matters he can influence following an impressive display in 'Der Klassiker'.
"We showed today that we can celebrate football. Over 90 minutes, we were four goals the better, so you can only praise the team," he said.
"We have done exactly what we set out to do. With the game on Wednesday, we have already shown that we have progressed defensively, and today we have defended forward.
"After, then we have played the football the spectators wanted to see."