Bayern, who won their Champions League group in each of the last four seasons, now lead Group C with 12 points from four games.
Their last-16 berth was secured by a wild 3-3 draw between Barcelona and Inter Milan in the other game in their section on Wednesday.
Thumped 5-0 by Bayern a week ago, Plzen found themselves trailing again after just 10 minutes in the Czech Republic.
Sadio Mane played a give-and-go with Goretzka to beat the Plzen defence and had no problems firing past Plzen goalkeeper Jindrich Stanek.
Julian Nagelsmann made six changes from the first meeting, using Joshua Kimmich and Thomas Mueller who had missed the home game because of Covid-19 infections.
Mueller scored Bayern’s second on 14 minutes with an easy tap-in after Kingsley Coman sprinted down the left flank and found him facing a wide open goal.
Goretzka scored the third into the bottom corner after Mueller’s low cross picked him out by the penalty spot on 25 minutes.
Ten minutes later, Goretzka chipped the ball over Stanek after a perfect through pass from Leroy Sane, turning the first half into a nightmare for the Czech underdogs.
But with nothing to lose, Plzen offered a much livelier performance in the second half.
Adam Vlkanova blasted in a headed pass from Jhon Mosquera on 62 minutes past Sven Ulreich, who had replaced the injured Manuel Neuer.
With 15 minutes to go, Jan Kliment fired home neatly on the turn from a pass from fellow substitute Libor Holik but Plzen were eliminated from the competition.
Bayern travel to Barcelona in the next round of games on October 26 while Inter host Plzen.