Bayern extended their advantage over second-placed RB Leipzig, who suffered a shock 3-2 defeat at second-from-bottom Mainz on Saturday.

As the only top-three team to win this weekend, European champions Bayern are firmly on course for a ninth consecutive Bundesliga title.

Thomas Mueller claimed the first of his two goals with a header before Lewandowski netted from a tight angle midway through the second half for his 23rd goal in 17 league matches this season.

Bayern then scored twice in the final two minutes, with a second Mueller header before David Alaba smashed in a long-range shot in the 90th minute.

"We have had a few big points this week -- even when we don't overrun the opposition," Mueller told Sky.

Bayern have taken a maximum nine points in the last week after a scrappy 1-0 win on Wednesday at Augsburg, who missed a late penalty, and a 2-1 home victory over Freiburg last Sunday.

Midfielder Joshua Kimmich weighed in with three assists in Gelsenkirchen.

Goalkeeper Manuel Neuer kept his 197th Bundesliga clean sheet to break Oliver Kahn's league record.

"I hope Schalke stay in the league and manage to turn the tide," said former Schalke player Neuer.

Schalke remain rooted to the bottom and 10 points from guaranteed safety.

Flick not 'completely satisfied'

However, Bayern coach Hansi Flick saw room for improvement.

"I wasn't completely satisfied. Sure, we scored four goals, but I also saw that we can do one or two things better in possession," said Flick.

"We sometimes play with too much risk, sometimes too slowly.

"Nevertheless, I'm satisfied with the nine points we got in one week."

Bayern routed the Royal Blues 8-0 in Munich when the teams last met in September, but the hosts put up more of a fight having changed their head coach three times in four months.

Even with captain Sead Kolasinac and veteran striker Klaas-Jan Huntelaar missing with leg injuries, they had chances as Suat Serdar and Mark Uth forced saves from Neuer.

Bayern broke the deadlock on 33 minutes when Kimmich was left with plenty of time to curl his cross straight into the path of Mueller.

Lewandowski once again proved why he was voted FIFA's best male player of 2020.

Kimmich lofted a pass over the Schalke defence, which Lewandowski controlled superbly, before beating two defenders and firing home from a tight angle nine minutes after the break.

Schalke goalkeeper Ralf Faehrmann had kept the score respectable with a string of saves until the dam burst with two goals in the final minutes.

A Kimmich free-kick presented Mueller with a second headed goal in the 88th minute, before Alaba's speculative shot from distance evaded Faehrmann's grasp.

Later, Hoffenheim jumped three places to 11th after their second straight win as Andrej Kramaric netted two penalties in a 3-0 home victory over Cologne, who remain in the bottom three.

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