Lewandowski's rich form continued at the Allianz Arena as he was involved in all three Bayern goals, scoring twice.
Having hit a hat-trick in last weekend's 8-0 mauling of Hamburg at home, Lewandowski's rich form continued at the Allianz Arena as he was involved in all three Bayern goals, scoring twice.
He is the Bundesliga's joint top-scorer with 19 goals, alongside Borussia Dortmund's Pierre-Emerick Aubameyang, having also scored six times in the Champions League and five in the cup.
"We managed to do everything we want to in the first-half and attacked well," said man-of-the-match Lewandowski.
"Schalke couldn't do much about it. We know one goal isn't enough in the cup, which is why we wanted more."
The Poland hot-shot gave holders Bayern the lead with just three minutes gone by deftly chipping Franck Ribery's pass over Schalke goalkeeper Ralf Faehrmann.
He the turned provider by supplying the cross for attacking midfielder Thiago Alcantara to head home on 16 minutes.
Lewandowski then drilled Ribery's pass into the Schalke net on 29 minutes for a seventh goal in his last four games.
Schalke defended well in the second half, but it was a miserable return to Munich for defender Holger Badstuber, on loan in Gelsenkirchen from Bayern until June.
The Germany centre-back was sent off late on for a second booking when he fouled Javi Martinez after pulling Arjen Robben's shirt moments before.
Schalke shot-stopper Faehrmann said Bayern's early goals were like a "punch in the face" for the Royal Blues.
"The first-half was nothing for us," he fumed. "We didn't put in the challenges and were behind in all areas.
"That is simply the class from Bayern that you can't allow any mistakes."
The win keeps Bayern on course for the treble of Champions League, Bundesliga and German Cup this season and was their third-straight dominant display in Munich.
Their Champions League Round of 16, first-leg 5-1 hammering of Arsenal, who they face away in Tuesday's return, was followed by the goal-bonanza against Hamburg.
Earlier, Borussia Moechengladbach booked their semi-final berth with a 2-1 win at Hamburg thanks to penalties by captain Lars Stindl and Brazilian striker Raffael.
Both Borussia Dortmund and third-division giant-killers Sportfreunde Lotte will go into the pot for the semi-finals after their clash on Tuesday was postponed by a heavy snowfall.
The referee deemed the playing surface in Lotte unsafe and the replay will take place on March 14.
The German Football Association (DFB) have reportedly advised Lotte to find an alternative ground given the poor condition of the pitch at their 10,000-capacity stadium.
Eintracht Frankfurt also reached the last four thanks to their 1-0 win at home to Arminia Bielefeld.
Midfielder Danny Blum scored Frankfurt's first-half winner.
However, the night belonged to ex-captain Marco Russ, who came off the bench in added time to make his first appearance since battling cancer last year.