Bayern were not allowed to settle into the game before the hosts shocked them, as Oleksandr Zubkov played an excellent through ball into the feet of Kevin, who charged into the box and without hesitation he slid the ball under Daniel Peretz to give his side the lead inside five minutes.
That shock lead didn’t last long however, as a dangerous ball into the Shakhtar box bobbled about the feet of several players before Konrad Laimer smashed the ball past Dmytro Riznyk to level the scores.
Despite the quick response, Bayern struggled to build on that and break down the home side’s stubborn defence, with Jamal Musiala trying his luck with a powerful shot, but the shot was blocked by a brave Shakhtar body.
With half-time approaching the visitors finally started to take control of the game, with Thomas Muller and Leon Goretzka both having chances blocked by Shakhtar bodies, as a second goal for the German side looked inevitable.
That goal finally came on the stroke of half-time, with Musiala calmly dribbling into the box and just as it looked like he might take the effort himself, instead he laid the ball into the centre of the box where Muller was lingering to smash the ball into the back of the net to give the visitor the lead.
The late goal prior to the break didn’t seem to knock the hosts' spirits, as Valerii Bondar nearly brought them level, but a Bayern player did just enough to prevent the ball from hitting the back of the net.
Bayern thought they had put the game to bed with 25 minutes left when Musiala found the back of the net, but the goal was ruled out for a foul in the box.
That seemed irrelevant moments later when Alaa Ghram caught Sacha Boey on the edge of the box to send Michael Olise to the spot, with the Frenchman firing his shot into the top left to double Bayern’s lead.
The visitors added a fourth with minutes left on the clock, as a loose ball fell to Musiala, who calmly placed the ball past Riznyk.
Olise rounded off the performance with his second of the night as the winger received the ball and flew past several defenders before wrong-footing Riznyk and tapping the ball into an empty net.
Despite their best efforts, Shakhtar have now lost four of their six matches in the Champions League with the Ukrainians facing an uphill battle to secure a play-off berth as they sit in 26th.
Meanwhile, Bayern will be happy to secure a vital win away from home, as they remain in the top eight with their sights on automatic qualification for the last 16.
Flashscore Man of the Match: Michael Olise (Bayern Munich)