In the club's first game back following the league's winter break, the hosts bossed this top vs bottom clash from start to finish, taking the lead in the 26th minute through Mario Mandzukic's fortunate opener.
The Croatian forward would add a second goal just past the hour mark to seal the win for Bayern, which maintains its nine-point lead at the top of the table over Bayer Leverkusen, while Furth remains rooted to the bottom and 10 points adrift of safety.
The Bavarians were on the attack right away through the threat of Frank Ribery, who was able to create danger down the flanks, even blasting one early effort into the side netting.
It was a clearly one-sided opening to the match, as all the possession – and the chances – fell the way of the home side.
Dante saw a shot from a great position charged down by the desperate Furth defense, before Mandzukic was thwarted in the 25th minute by a sublime save from Wolfgang Hesl at his near post.
But Hesl was to turn from hero to villain in an instant. Mandzukic’s half-volley from Thomas Muller’s cross was too hot to handle for the Furth keeper, who spilled his catch clumsily into the back of the net.
And with 35 minutes gone, Bayern could have been further in front had Muller and Mandzukic found the target with a pair of gilt-edged opportunities.
The second half continued in much the same vein as the first, with the home side comfortable and clearly in control, if not entirely clinical in front of goal.
However, the club was given a scare eight minutes after the restart, when Zoltan Stieber’s low cross was cleared away from danger at the last by Dante, with players lining up to tap it home.
The hosts were soon back on the attack, though, with Bastian Schweinsteiger forcing Hesl to tip his drive over the bar with a fine save. But from Toni Kroos’ resulting corner, Mandzukic headed past Hesl at his near post for his and his side's second of the afternoon.
Heynckes' men could have scored again in the time that remained, with substitute Arjen Robben proving a particular threat to a tired visiting defense, but no more goals were forthcoming as Furth managed to avoid a thrashing.