Anthony Modeste gave Hoffenheim the lead midway through the first half as the newly crowned champions suffered a title-winning hangover at the Allianz Arena, but two goals from Claudio Pizarro and a Xherdan Shaqiri strike appeared to have given Pep Guardiola's men a commanding lead.
Hoffenheim had other ideas, though, and Sejad Salihovic pulled a goal back before the break before Roberto Firmino earned the visitors a point in the second half, making them only the third side to take anything off Bayern in the Bundesliga all season with a 3-3 draw.
Reus, meanwhile, struck once before the interval and twice after to hand Dortmund a nail-biting 3-2 victory over their relegation-threatened hosts, who had led through goals from Christian Gentner and Martin Harnik.
Stuttgart's cause was not helped by the dismissal of Georg Niedermeier, having conceded the penalty which led to Reus' second goal.
The visitors' win moved them back a point above Schalke, who had temporarily taken over second place with a 2-0 triumph over Hertha Berlin on Friday night.
Elsewhere, Bayer Leverkusen were jeered off the field by their own fans at the BayArena after being held to a 1-1 draw by bottom-placed Eintracht Braunschweig.
Ken Reichel gave the visitors the lead early in the second half before a penalty from Stefan Kiessling saved the hosts from an even worse result.
They nevertheless saw their advantage over fifth-placed Wolfsburg reduced to a single point, jeopardising their hopes of qualifying for the Champions League next season, and drawing derision from their own fans.
Wolfsburg defender Naldo scored a stunning winning goal in the final minute to hand the Champions League-chasing Wolves a 2-1 success against Eintracht Frankfurt.
The Brazilian powered home from around 45 yards as the hosts turned around a 1-0 deficit to take all three points. Ivica Olic had levelled for Dieter Hecking's side after they had gone behind to Stefan Aigner's goal.
Mainz picked up three points in the battle for a European spot with a 3-0 triumph over fellow surprise package Augsburg.
Goals from Niko Bungert, Marwin Hitz (own goal) and Johannes Geis handed Thomas Tuchel's team their first win in three games.
Elsewhere, Freiburg picked up a crucial 3-2 win over fellow strugglers Nurnberg to move five points clear of the Bundesliga relegation zone on Saturday evening.
Emanuel Pogatetz gave Nurnberg the lead against the run of player in the seventh minute before Pavel Krmas levelled. A penalty from Josip Drmic restored the hosts' lead at half-time, after Freiburg had hit the post twice.
But Admir Mehmedi brought Freibug level with a penalty eight minutes into the second half and Felix Klaus then sealed a deserved victory for Freiburg.