Record-breaker Mueller steals the show from Lewandowski and even Messi
Mueller netted twice in Lisbon as Barcelona conceded four goals in the first-half of a Champions League game for the first time as Bayern went 4-1 up at half-time.
Substitute Philippe Coutinho also scored twice in Bayern's 8-2 hammering.
The 30-year-old Mueller capped an outstanding display by passing Philipp Lahm's record to become the German with the most Champions League appearances on 113 games.
In the build up, there had been fierce debate as to whether Lewandowski or Messi is the better player.
However, it was Mueller who stole the show, underlining his status as Barcelona's nemesis with six goals in five games against the Spanish giants.
Mueller scored against Barcelona when Bayern bowed out in the Champions League semi-finals in 2014/15.
He also netted three goals over two legs against Barcelona seven years ago when Bayern romped to a 4-0 win in Munich and 3-0 away in the semi-finals on the way to winning the 2013 Champions League title.
After creating a record 21 assists in the Bundesliga last season - many of them finished by Lewandowski - Mueller outshone the Champions League's top-scorer this season in Lisbon with two superb first-half goals.
He took a return pass from Lewandowski with just four minutes gone to fire past Barca's Germany goalkeeper Marc-Andre Ter Stegen.
After Bayern defender David Alaba turned the ball into his own net on seven minutes, Bayern emphatically re-established their lead by bossing the Barca midfield with goals by Ivan Perisic and Serge Gnabry.
Mueller made it 4-1 on 31 minutes when he fired in Joshua Kimmich's low cross at the far post to leave Barcelona shell-shocked at the break.
His form in 2019/20 had already proved that Germany head coach Joachim Loew arguably wrote Mueller out of his plans far too soon.
Following Germany's disastrous 2018 World Cup campaign, when the holders went out in the group stages, Mueller was unceremoniously dumped by Loew in March 2019 alongside defenders Mats Hummels and Jerome Boateng.
However, Mueller has responded by making a mockery of Loew's decision and proven emphatically why former Bayern coach Niko Kovac was wrong to start him on the bench this season.
When Kovac was sacked in November, his replacement Hansi Flick reinstated Mueller, who has been a key factor with 14 goals this season.
He has been the central cog in attack as Bayern romped to an eighth straight Bundesliga title, lifted the German Cup and remain on course to add the Champions League title.