Pep Guardiola’s Bayern have already claimed their last 16 place as group winners with two Champions League games to spare and have now opened an ominous gap in the German league.
Mario Goetze and Robert Lewandowski scored first-half goals at Munich’s Allianz Arena as the hosts cruised into the lead.
Germany captain Bastian Schweinsteiger made his first appearance of the season off the bench, 132 days after the World Cup final, as Bayern scored twice in the last 10 minutes through Arjen Robben and Sebastian Rode.
“We had problems at the start with our build-up play and we only found our game midway through the first-half, so I think the 4-0 result was too high,” said an unimpressed Guardiola.
Bayern’s iron grip on this season’s league title was tightened by results elsewhere as they extended their 21-match unbeaten run.
Second-placed Wolfsburg had their eight-match winning streak ended at Schalke while third-placed Borussia Moenchengladbach also lost ground with a 3-1 defeat at Eintracht Frankfurt to fall 10 points behind the Bavarians.
Schalke boss Roberto di Matteo warmed up for Tuesday’s visit of his former club Chelsea, who sacked him in 2012 just six months after winning the Champions League, with a 3-2 victory over Wolfsburg.
Schalke raced into a 3-0 lead with fewer than 30 minutes gone as Eric Choupo-Moting fired his side into an early lead, then added a second on 22 minutes.
Wolfsburg’s defence completely failed to deal with Christian Fuchs’ free-kick which bounced over goalkeeper Diego Benaglio and into his goal three minutes later to leave Wolves reeling.
The visitors pulled a goal back just before the break when Croatia’s Ivica Olic fired home from close-range on 37 minutes before ex-Arsenal forward Nicklas Bendtner made it 3-2 with 16 minutes left, but the win puts Schalke sixth.
Ten-man Borussia Moenchengladbach slumped to a second straight defeat after Norway midfielder Havard Nordtveit had given them a sixth-minute lead before Frankfurt hit back to claim a 3-1 win.
– Reus suffers fresh injury –
Borussia Dortmund, who have already qualified for the Champions League’s last 16, threw away a two-goal lead to draw 2-2 at Paderborn ahead of Wednesday’s clash at Arsenal to stay a point above the relegation spots.
Having dominated with first-half goals by Germany winger Marco Reus and Gabon’s Pierre-Emerick Aubameyang, Dortmund slumped again as Paderborn’s Lukas Rupp pulled a goal back before Mahir Saglik’s 81st-minute equaliser.
There was more bad news for Dortmund boss Jurgen Klopp on 65 minutes when Reus, who has only just returned from injury, was carried off after twisting his right ankle after a heavy tackle.
“Because of Marco’s injury, I find it hard to talk about football,” said Klopp.
“I have no problem to play out a draw here and I have huge respect for Paderborn, but this wasn’t a good day for us.”
Hertha Berlin’s 2-1 victory at Cologne, thanks to Cameroon midfielder Marcel Ndjeng’s late winner on Saturday evening, means Dortmund remain 15th in the league after losing seven of their 12 games so far this season.
Bayer Leverkusen, who host Monaco as leaders of their Champions League group on Wednesday, warmed up with a 3-1 win at Hanover 96.
Stefan Kiessling, South Korea star Son Heung-Min and Germany’s Karim Bellarabi scored while Hanover’s midfielder Ceyhun Gulselam headed home Japan midfielder Hiroshi Kiyotake’s free-kick with half-an-hour on the clock.
Mainz drew 2-2 with Freiburg.
On Sunday Hamburg host Werder Bremen in the north Germany derby with both teams in the bottom three.