The result put Munich three points clear of their battered opponents at the top of the German league table.
Coach Carlo Ancelotti hailed a "perfect" first half in which Bayern's Thiago Alcantara and Xabi Alonso scored early goals before Leipzig winger Emil Forsberg was shown a red card for a dangerous tackle. That left the visitors to play an hour at Munich's Allianz Arena a man down.
Leipzig goalkeeper Peter Gulacsi then conceded the penalty which Lewandowski converted on 45 minutes to put Bayern 3-0 up at the break.
The result put Munich three points clear of their battered opponents at the top of the German league table heading into the winter break.
Leipzig briefly knocked Bayern off top spot early this month and the two have been in a neck-and-neck battle since.
Ancelotti highlighted his side's first half display.
"We were very aggressive and quickly established control, which gives us self-confidence, but we must still improve," said the Italian.
There was a minute's silence for the victims of Monday's truck attack in Berlin at Munich, Cologne, Ingolstadt and Hoffenheim, but it was most poignant at the capital's Olympic stadium.
Hertha Berlin hosted Darmstadt seven kilometres (four miles) from Breitscheidplatz where a lorry ploughed into a busy Christmas market on Monday, leaving 12 dead and at least 48 injured.
Fans in Berlin held up thousands of lights during a poignant minute's silence before kick off. The Hertha squad had earlier laid a wreath at the site.
A second-half free-kick by Marvin Plattenhardt and a Salomon Kalou header sealed Hertha's 2-0 win to stay fourth.
In Munich, Ancelotti pulled a surprise by leaving Germany forward Thomas Mueller and French winger Franck Ribery on the bench.
Thiago Alcantara and Douglas Costa started and the selection paid off with 17 minutes gone.
Captain Philipp Lahm fired in a cross, Lewandowski hit the post, but Thiago was waiting in the middle to convert the rebound.
A mistake by Leipzig's Naby Keita, who had recovered from a thigh injury, saw Bayern grab their second on 25 minutes.
Arturo Vidal robbed the Guinea midfielder of possession, Lewandowski sprinted clear and Thiago slipped the ball to Alonso, who fired home.
A header by Leipzig captain Willi Orban forced Bayern goalkeeper Manuel Neuer into a diving save just before disaster struck for the visitors on 30 minutes.
Left winger Forsberg was sent off when his tackle caught Philipp Lahm on the Achilles tendon and referee Felix Zwayer pulled out a red card.
"He knew straight away that he had made a mistake, he's already apologised and we all can make mistakes," said Leipzig coach Ralph Hasenhuettl.
Gulacsi then conceded the penalty as it finished 3-0 at the break.
Bayern were then to let their opponent chase the ball as they enjoyed 75 percent possession, but the hosts battered the Leipzig goal in the closing minutes.
"I am proud of what the team has achieved this season, but this was a lesson for us and compliment to Bayern on the way they played," added Hasenhuettl.
Hoffenheim, the only unbeaten team in Germany's top flight, stay third after their tenth draw in 16 games as it finished 1-1 at home to Werder Bremen.
Hoffenheim's striker Sandro Wagner claimed his ninth league goal this season before Bremen's ex-Arsenal winger Serge Gnabry rescued a point.
Cologne striker Anthony Modeste gave his side a first-half lead before Bayer Leverkusen's Brazil defender Wendell equalised in a 1-1 draw.
Ingolstadt remain second from bottom after their 2-1 home defeat to mid-table Freiburg, for whom Florian Niederlechner netted twice.