Muller, 30, started for the Bavarians on Friday in their quarter-final clash in Lisbon's Estadio da Luz, as they vied with Barca for a place in the semi-finals of the European competition.
It was the forward's 113th Champions League appearance, setting a new German record ahead of former Bayern team-mate Philipp Lahm.
Barca have more often than not struggled to contain Muller's talents, and so it proved again as he opened the scoring almost immediately after the quarter-final clash began.
Muller linked up with Robert Lewandowski to fire past Marc-Andre ter Stegen, netting in the process his fifth goal against the Catalans — a feat managed only by Andriy Shevchenko in the Champions League.
5 - Thomas Müller has scored five goals in five appearances against Barcelona in the Champions League - only Andriy Shevchenko has scored as many goals against them in the competition (also five). Instinct. #UCL pic.twitter.com/Cp1oPmKyje— OptaJoe (@OptaJoe) August 14, 2020
Bayern's early lead proved short-lived, as David Alaba sliced a Jordi Alba cross past Neuer to level the scores with just seven minutes on the clock.
But with both sides throwing men forward and demonstrating some rather suspect defending, it was the Bundesliga champions who went on to take advantage in the first half.
Ivan Perisic and Serge Gnabry both scored in quick succession to restore Bayern's advantage, before Muller popped up again to put his side 4-1 up inside the opening half-hour - taking his own tally against Barca to a record six.
Perhaps the only real surprise in Lisbon was that, of Die Roten's four opening goals, Champions League top scorer Lewandowski had not hit a single one.
The Poland international did have a hand in Muller's opening strike, though, marking an impressive feat of his own.
Lewandowski now heads not only the competition's goal charts, with 13, but has also managed five assists, more than anyone else in the current edition.