An Arjen Robben hat-trick helped Bayern Munich open up a 20-point lead at the top of the Bundesliga with a 5-1 win over ten-man Schalke 04, who suffered a second drubbing in four days.

Having lost 6-1 at home to Cristiano Ronaldo's Real Madrid on Wednesday in the Champions League, Schalke were put to the sword again at Munich's Allianz Arena as Bayern went 4-0 up inside half-an-hour.

Bayern extended their record unbeaten league run to 48 matches, dating back to October 2012, and earned their 15th straight league victory.

"My son will enjoy having the match ball, my kids are my biggest fans," said Dutch winger and father of three Robben.

"We play with so much aggression and tempo, we really put our foot down.

"The title is getting every closer, we played with so much passion, which we need for the big games, especially in the Champions League."

With just three minutes gone, left-back David Alaba netted a free-kick, then Robben scored either side of Mario Mandzukic's header from a superb Alaba cross to make it 4-0 at the break.

Schalke were gifted a goal when Jefferson Farfan's corner was turned into his own net by Munich right-back Rafinha, in for captain Philipp Lahm, with 25 minutes left.

To compound Schalke's misery, Greece centre-back Kyriakos Papadopoulos was shown a straight red for bringing down Mandzukic in the area.

His foul allowed Robben to wrap up his hat-trick with a 77th-minute penalty.

"You can't get much worse than that," fumed Schalke captain Benedikt Hoewedes, who had a miserable 26th birthday.

"That was highly embarassing and we need to apologise to our fans.

"We gave them way too much respect."

Coach Pep Gurdiola flippantly told reporters "don't ask me about the title" in broken German on Friday, but with 11 league games left, Bayern can wrap up their 24th German league title by the end of March at the latest.

Earlier, Borussia Dortmund built on their midweek Champions League victory over Zenit St Petersburg by going second with a 3-0 win at home against Nuremberg.

Jurgen Klopp's side backed up Tuesday's 4-2 win in Russia to leapfrog Bayer Leverkusen, who crashed 1-0 at home to Mainz, their fifth straight defeat and eighth loss in 10 games.

Dortmund's Germany defender Mats Hummels celebrated his first game in four weeks after a foot injury by netting the opener at Borussia's Westfalenstadion.

Turkey midfielder Nuri Sahin fired in a free-kick and after Robert Lewandowski's header was saved, Hummels tapped home the rebound just after the break.

Poland star Lewandowski then scored his 15th league goal of the season by converting a superb pass from Henrikh Mkhitaryan on 64 minutes before the Armenia international netted his second goal in four days seven minutes from time.

Leverkusen's dreadful form continued with their fourth straight home defeat as Mainz moved up to sixth with their fifth win in eight games.

Ex-Liverpool star Sami Hyypia is facing a crisis as his third-placed Leverkusen side last won on February 1 and were also routed 4-0 at home to Paris Saint-Germain in the Champions League.

Cameroon striker Eric Choupo-Moting slammed home the winner past goalkeeper Bernd Leno on 37 minutes.

A horrendous error by Germany goalkeeper Marc-Andre ter Stegen cost Borussia Moenchengladbach their place in the top six following a 1-1 draw at bottom side Eintracht Braunschweig and left them winless in their last eight games.

Braunschweig gifted Gladbach a first-half lead when Iran goalkeeper Daniel Davari turned the ball into his own net with half an hour gone.

But Ter Stegen, who has been linked with a move to Barcelona next season, could only watch in horror as the ball spun into his own net after he failed to control a back pass from captain Filip Daems.

There was trouble before Werder Bremen's 1-0 win over Hamburg in the north German derby as the visitors' bus was pelted by Bremen fans, breaking a window.

Police used water cannons to separate rival fans outside Bremen's Weser Stadion and eight supporters were arrested.

Bremen grabbed an early winner when Austria midfielder Zlatko Junuzovic fired home after a spectacular back-heel from team-mate Aaron Hunt and the defeat left Hamburg third from bottom while Bremen climb to 12th.

Hanover's Senegal striker Mame Diouf scored his first goal for a month in his side's 1-1 draw at Augsburg.