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|Lewandowski is up to 38 goals for the season in all competitions. (Photo: AFP/Odd Andersen)|
Mueller struck 12 minutes after his half-time introduction before Lewandowski doubled the lead and Sebastian Rudy added a third as coach Jupp Heynckes started a weakened team.
"All in all, we played excellent football," beamed Heynckes.
"The team is in top form, regardless of who plays and in what position.
"When you have a Champions League game on the horizon, it's important to win league games like this."
With an eye on Wednesday's blockbuster Champions League semi-final first leg at home to Real, Heynckes left out several regulars while handing 18-year-old centre-back Lars Lukas Mai his Bundesliga debut.
Both sides had their chances in a goalless first half before Bayern pulled away.
After Mueller replaced Arjen Robben, the Germany international struck on 57 minutes when his first-time shot from a Juan Bernat cross deflected off Salif Sane and past goalkeeper Philipp Tschauner.
Bayern's top scorer Lewandowski added a second just six minutes after coming on himself for his 38th time this season in all competitions.
Defensive midfielder Rudy capped the win a minute from time to leave Bayern 23 points clear of second-placed Schalke, who are at bottom side Cologne on Sunday.
Later Jadon Sancho and Marco Reus inspired Borussia Dortmund to a 4-0 romp at home to Bayer Leverkusen.
Even with striker Michy Batshuayi sidelined by an ankle, the pair shone in front of goal.
Sancho, 28, a former Manchester City winger, leapt for joy after becoming the youngest Englishman to score in the Bundesliga when he hit the bottom corner with 13 minutes gone.
Reus had a goal disallowed and a penalty saved before grabbing the second, moments after hitting the bar, from a superb pass from World Cup winner Mario Goetze.
Sancho set up Maximillian Philipp to tap home Dortmund's third on 63 minutes.
The English teenager then supplied a cross for Reus to head home his second on 79 minutes to cap a superb display.
"The 1-0 (lead) gave us self-confidence. I hit the penalty very weakly, which made me want to help the team even more in the second-half," said Reus.
Having been left out of last month's friendlies against Spain and Brazil, Reus boosted his World Cup chances in front of Germany head coach Joachim Loew.
The result means Dortmund consolidate third place and stay three points ahead of Leverkusen.
Ten-man RB Leipzig crashed to a 5-2 home defeat by Hoffenheim in a key clash for the Champions League places next season.
Swedish international Emil Forsberg was sent off for a foul on Florian Grillitsch just after the break with Hoffenheim already 3-0 up.
Mark Uth, Serge Gnabry and Pavel Kaderabek all scored as Leipzig's defence buckled in the opening 45 minutes.
Naby Keita pulled a goal back before the hour mark, but Uth scored his second goal with a header before midfielder Lukas Rupp hit Hoffenheim's fifth.
England Under-21 international Ademola Lookman, on loan from Everton, set up Dayot Upamecano to score Leipzig's second on 88 minutes.
The result leaves Hoffenheim fifth, just two points from the Champions League places, while six-placed Leipzig are four adrift.
Mid-table Hertha Berlin romped to a 3-0 win at German Cup finalists Eintracht Frankfurt as Davie Selke, Mathew Leckie and Alexander Esswein scored.
Frankfurt suffered a cup hangover, after beating Schalke in Wednesday's semi-final, and remain seventh.
Club captain Christian Gentner and Berkay Ozcan scored Stuttgart's goals in their 2-0 victory over Werder Bremen.
Ex-Tottenham Hotspur midfielder Lewis Holtby boosted Hamburg's hopes of avoiding relegation in their 1-0 win at home to Freiburg.
Holtby jinked through the Freiburg defence and tapped home just after the break to leave second-from-bottom Hamburg five points from safety with three games left.
Hamburg are the only current Bundesliga to have played in every season since its foundation in 1963.
Collated German Bundesliga results on Saturday:
RB Leipzig 2 Hoffenheim 5
Eintracht Frankfurt 0 Hertha Berlin 3
Hamburg 1 Freiburg 0
Hanover 0 Bayern Munich 3
VfB Stuttgart 2 Werder Bremen 0
Borussia Dortmund 4 Bayer Leverkusen 0