With the pressure on them to put in a performance after a disappointing loss on the weekend, United would have surprised a few with their start as they were the better side, not allowing their opponents to get into their rhythm.
The Red Devils were almost rewarded for their positive start as Christian Eriksen fired a ball across the face of goal but as Alphonso Davies beat Facundo Pellistri to the ball, it returned to the feet of the Dane but his goalbound effort was saved off the line by Sven Ulreich.
Bayern took a while to get going but when they did, they punished United with two goals in four minutes.
The star forward dribbled through the United defence before picking out an unmarked Serge Gnabry in the box who finished into the far corner.
After having all their good work undone in a four-minute spell, it was a case of getting to half-time without conceding again for United.
Once more the visitors started the half positively and this time they found the back of the net as Bayern failed to clear the ball, allowing Casemiro to play Rashford through but instead of shooting, he laid it off to Rasmus Hojlund to fire in his first United goal via a deflection.
However, just like in the first half, Bayern were presented with a gift as Eriksen was penalised for handling in the box.
Harry Kane stepped up and clinically buried the spot-kick for his sixth goal against the Red Devils.
Bayern could smell blood, and almost added a fourth but Sane was denied by the woodwork after being brilliantly picked out by Musiala.
United struggled to fashion a response after Bayern restored their two-goal lead, but they were given a lifeline late on as Casemiro did well to win the ball in the box and poke the ball past Ulreich, setting up a tense finish.
But once again, Bayern had a response and made them pay, wrapping up the victory as Mathys Tel showed great composure in the box, taking a touch and firing into the roof of the net.
Sensationally, United had one final reposte as Casemiro turned home a Bruno Fernandes free-kick, but Erik ten Hag's men had no time to level the scores as Bayern were victorious in a UCL classic.
Flashscore Man of the Match: Jamal Musiala (Bayern Munich)