Robert Lewandowski scored a brilliant first-half hat-trick following the sending off of Alphonso Davies to secure all three points for his side. He opened the scoring following some brilliant work on the left by Serge Gnabry.
Minutes later, the winger scored Bayern Munich's second of the night by capping off a brilliant team move. The Polish international popped in with two more goals to complete his hat-trick as Bayern Munich registered an impressive clean sheet despite a numerical disadvantage.
On that note, let's have a look at the player ratings for Bayern Munich.
Manuel Neuer - 7.5/10
Manuel Neuer had a decent outing. He made some decent saves to dent Stuttgart's hopes of a comeback as the German international registered a well-deserved clean sheet.
Benjamin Pavard - 7.5/10
Benjamin Pavard put in a great performance at the back. The Frenchman was assured both offensively as well as defensively. The Bayern defender made four interceptions and recovered possession for his side seven times during the match.
Jerome Boateng - 7.5/10
Jerome Boateng was rock solid at the back for Bayern Munich, leading the backline impressively after his side were down to ten men. Boateng made nine recoveries, won six duels, made five clearances and won two tackles.
Niklas Sule -7/10
Niklas Sule combined well with Jerome Boateng at the heart of the Bayern Munich defence. The duo ensured that nothing went past them. Sule was quite composed at the back and was successful in foiling every attack that came down his side.
Alphonso Davies - 5.5/10
Alphonso Davies had his night cut short when he was sent off in the 12th minute of the game. The Canadian was red-carded for a reckless challenge on Wataru Endo.
Leon Goretzka - 7.5/10
Leon Goretzka was the engine room of Bayern Munich against Stuttgart. He did all the dirty work for his side in the centre of the pitch. Goretzka won eight duels, made three clearances, won two tackles and made ten recoveries for his team.
David Alaba - 7.5/10
David Alaba put in a massive shift for Bayern Munich, covering a lot of ground to protect the left flank after Davies' sending off. He aced as a pseudo left-back. Alaba won three duels, made seven clearances, won two tackles and made nine recoveries on the night.
Leroy Sane - 7.5/10
Leroy Sane kept the opposition defenders on their toes, terrorising them with his blistering pace down the right flank. The 25-year-old set up Gnabry for Bayern Munich's second of the night.
Thomas Muller - 8.5/10
Thomas Muller had a great outing. The Raumdeuter created trouble for the visitors by sending in perfect through balls. Muller created the most chances for his side (6) and won six duels during his stay on the pitch. He also to set up Lewandowski's second goal of the night.
Serge Gnabry - 8/10
Serge Gnabry combined well with Thomas Muller and Robert Lewandowski high up the pitch. The German international scored Bayern Munich's second goal of the night. He also set up his side's opener after some solid work on the left flank.
Robert Lewandowski - 9.5/10
Robert Lewandowski was electric for Bayern Munich. The Polish international scored a perfect first-half hat-trick to seal the deal for the Bavarians as he took his goal tally for the season to 42.
Lewandowski has now scored 35 Bundesliga goals in 26 games as he closes in on Gerd Muller's record of 40 goals.
Ratings of Bayern Munich Substitutes
Kingsley Coman - 6.5/10
Kingsley Coman came on for Gnabry in the 60th minute. The Frenchman tried to do something fancy but failed to produce the desired end product.
Eric Maxim Chupo-Moting - 6.5/10
Eric Maxim Chupo-Moting had a powerful impact after coming on for Lewandowski. He came close to scoring on a couple of occasions as well.
Javi Martinez - N/A
Javier Martinez did not have much impact on the game.
Jamal Musiala- N/A
Jamal Musiala came on too late to merit a rating.