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 UEFA 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.
Freiburg boost survival hopes
In the late kick-off, Freiburg boosted their survival hopes with a come-from-behind 3-2 victory over fellow strugglers Nurnberg.
Christian Streich's side, heading into the game on a three-match unbeaten run, trailed at the break, Josip Drmic's penalty on the stroke of half-time having restored the visitors' lead after Emanuel Pogatetz's early strike had been cancelled out by Pavel Krmas.
But Admir Mehmedi got the hosts back on level terms from the penalty spot within eight minutes of the restart and Felix Klaus put them ahead for the first time 12 minutes later, with Pogatetz's last-minute dismissal compounding Nurnberg's misery. The result saw Freiburg pull three points clear of Nurnberg, who sit just two points better off than 16th-placed Hamburg and 17th-spotted Stuttgart.