A Joshua Kimmich own goal had given the Portuguese outfit a shock lead in the 54th minte but the German champions roared back into the contest.
Serge Gnabry netted the equaliser in the 65th minute, volleying in Michael Olise's corner.
Karl then put the home team ahead just four minutes later, to follow on from the 17-year-old's goals earlier in the continental competition against Club Brugge and Arsenal.
Jonathan Tah then sealed the contest with 13 minutes remaining, with Kimmich's cross headed back across goal by Gnabry for the defender to finish first time into the net.
The victory sees Bayern move up to second in the Champions League table, although it is still very early in the tournament to make any bold predictions.
Erling Haaland has given a confident update on his Manchester City future, stressing his commitment to the club's long-term project while accepting the uncertainty around Pep Guardiola's contract beyond 2027.
Tottenham's hopes of welcoming Dominic Solanke back any time soon have taken a major hit, with a trusted club insider revealing that the striker may not return until February.
Reece James has stepped up Chelsea's preparations for Saturday's meeting with Everton at Stamford Bridge, with the captain leading internal discussions as the Blues try to halt their worrying run of form.
Kylian Mbappe's race to be fit has taken another hit, with the French forward facing a serious battle to return for Real Madrid after remaining unused in their 2-1 defeat to Manchester City at the Bernabeu.
