A 5-0 thrashing of Besiktas in the first leg of their Champions League last-16 tie means Bayern have now won 14 games in a row to match a club milestone from 1980.
And the signs were ominous as soon as Muller had given Jupp Heynckes' side the lead before the end of the first half.
Bayern had already been put in an advantageous situation just 16 minutes into the contest as a bad Atiba Hutchinson back pass was picked off by Robert Lewandowski. Besiktas' Domagoj Vida brought the striker down, earning him a red card for a denial of clear goal-scoring opportunity.
With two minutes of the first half remaining, Kingsley Coman broke through down the left and crossed into the area. David Alaba didn't strike his shot well, but the ball fell to Muller to score after he had been played onside by Besiktas right-back Adriano.
Once Muller scored, Besiktas faced the unenviable task of trying to become the first team to defeat Bayern when the Germany international finds the back of the net. 61 sides had tried and 61 had failed previously, with the best result achieved by three teams who managed a draw.
But it was not to be for Besiktas. Coman turned goalscorer from Lewandowski's assist early in the second half to double the advantage for the hosts.
And then Muller doubled his fun in the 66th minute as he poked home a Joshua Kimmich cross to make it 3-0 to Bayern, and ensure the streak moved to 62.
61 - Bayern Munich are previously unbeaten in their last 61 competitive matches that Thomas Müller has scored in (W58 D3). Formality. pic.twitter.com/qkfzdn4Tgu— OptaJoe (@OptaJoe) February 20, 2018
Lewandowski added a fourth for good measure late in the second half and then picked up the club's fifth when Muller set him up for the brace.
Besiktas will get their chance to overturn the massive deficit on March 14 when they face Bayern at home in the second leg of the tie.