Bayern bag five, Dortmund into second
Having secured their place in the knockout phase of the UEFA Champions League in midweek with a draw at Valencia, Bayern ran riot at the Allianz Arena and added a point to their lead.
Bayern set another Bundesliga record of 34 points after the first 13 games and the hosts took the lead with only four minutes gone when Spain midfielder Javi Martinez netted his first goal since his August transfer from Athletic Bilbao.
The third came on 37 minutes when France winger Franck Ribery fired home, while Brazil centre-back Dante made it 4-0 when he met Kroos' free-kick at the far post on 63 minutes.
Germany striker Mario Gomez needed less than 30 seconds to claim the fifth, having come off the bench on 67 minutes.
Dortmund came from behind at Mainz to claim their third straight away win. They fell behind on four minutes when Marco Caligiuri put the hosts ahead, but Germany midfielder Marco Reus equalised when he hit the top corner eight minutes later.
Dortmund took the lead just before the break when Mario Gotze put Poland striker Robert Lewandowski into space to flick the ball over the Mainz goalkeeper to claim the three points and second place from neighbours Schalke.
The Royal Blues dropped to third after drawing 1-1 with Eintracht Frankfurt, who are fourth, in Gelsenkirchen. Dutch striker Klaas-Jan Huntelaar opened the scoring on 11 minutes, but the lead lasted just 105 seconds as Stefan Aigner headed the visitors level.
Frankfurt were reduced to ten men when Karim Matmour was dismissed for a second yellow card on 87 minutes.
Wolfsburg held Werder Bremen to a 1-1 draw as Wolves director of sport Klaus Allofs met the north German team he left earlier this month after 13 years.
Werder took the lead after Austria striker Marko Arnautovic scored on 35 minutes, but after defender Lukas Schmitz was sent off for a second yellow card on 62 minutes, Dutchman Bas Dost equalised on 64 minutes.
Nurnberg had Markus Feulner sent off after just 35 minutes when he flew into a two-footed tackle, while Turkey midfielder Sercan Sararer was dismissed for a second yellow card on 61 minutes.