Thomas Muller opened the scoring before Joshua Kimmich doubled their advantage.
Bayern were reduced to 10 men after the break when Benjamin Pavard was sent off, but they added a third through a Sebastian Griesbeck own goal.
Furth scored late on but Bayern move three points clear of Wolfsburg.
Victory for the champions is their fifth in a row, in a thrilling run which has seen them score 29 goals in their last six games in all competitions.
Apart from Pavard’s sending-off, the only negative for Bayern was Robert Lewandowski’s failure to equal Gerd Muller’s consecutive goals record.
The Polish striker had scored in his last 15 league matches, and nearly drew level with Muller on 16 but Bayern’s third was awarded as a Griesbeck own goal.