Muller, Heynckes buoyed by Bayern Munich's edgy victory
Muller's 79th-minute effort proved enough for Bayern to claim all three points from a dramatic encounter, with goalkeeper Sven Ulreich pulling off a stoppage-time penalty save to deny his former a club a share of the spoils.
The victory puts Bayern further into the distance at the Bundesliga summit heading into the mid-season break, with the DFB-Pokal third-round clash with Borussia Dortmund their final match of 2017.
And Muller, who replaced Corentin Tolisso in the 65th minute, says the triumph displayed Bayern's grit under Jupp Heynckes.
"Stuttgart played unpleasantly, man against man almost all over the place," Muller is quoted as saying by Bayern's official website.
"We did well against it. We are happy about the 1-0, they had the penalty in the last second, but of course we should have made it 2-0 before then.
"Now we have won 1-0 three times in a row. It's not like we are playing brilliantly, but we have the quality and the cleverness to get results, even when things are not going so well."
#Ulreich: "It was already a special game against my old club and then came that ending - it really was an explosion of emotion!" #VfBFCB pic.twitter.com/7M06GyJ6O6
— FC Bayern English (@FCBayernEN) December 16, 2017
Bayern boss Heynckes saw his side create plenty of chances at the Mercedes-Benz Arena, though it was not until late that Muller found a way past Stuttgart goalkeeper Ron-Robert Zieler.
The defeat leaves Stuttgart 14th, two points above the relegation play-off place, and the Bavarian giants' coach was relieved to have come through a difficult fixture with all three points.
"The game had all the ingredients, it was very interesting, intense and dramatic," Heynckes said.
"Both teams have played great. I cannot understand why Stuttgart do not have more points.
"Now the players have to recover and get their heads free, then I'm confident that we can beat Borussia Dortmund."