Reus begins farewell tour while Bayern stumble in Stuttgart
Late goals from South Korea's Jeong Woo-yeong and the DRC's Silas Katompa Mvumpa saw Bayern suffer their first defeat in Stuttgart since 2007.
Stuttgart took the lead with a smash-and-grab goal just before the half-hour mark, Leonidas Stergiou prodding home after a dainty chip over the back line from Deniz Undav.
Bayern then equalised in controversial circumstances, after Stuttgart captain Waldemar Anton conceded a penalty with a very light challenge on Serge Gnabry.
Harry Kane converted the resulting penalty, taking his season tally to 36 goals, moving to within just four of Robert Lewandowski's Bundesliga record.
But an 83rd minute header from Jeong put Stuttgart back in front before Silas sealed the win in stoppage time.
While Bayern head to Madrid with their tails between their legs, fellow Champions League semi-finalists Dortmund were in fine form ahead of their trip to Paris Saint-Germain on Tuesday.
Ovations for Reus
It was a particularly emotional afternoon for Reus, who had announced on Friday that after 12 years at Dortmund he would leave at the end of the season.
Youssoufa Moukoko gave Dortmund the lead early on, flicking the ball in from close range after some chaotic defending from Augsburg.
Donyell Malen doubled the lead on 20 minutes, heading home an inswinging corner from English winger Jamie Bynoe-Gittens.
Moukoko added another from a corner shortly afterwards, before Ruben Vargas pulled one back for Augsburg against the run of play.
Dortmund remained unfazed, however, and Reus soon made it 4-1 with an elegant chip over goalkeeper Alexander Meyer.
Reus then set up Felix Nmecha for Dortmund's fifth in the second half, and hit the bar himself before leaving the pitch to standing ovations on 65 minutes.
Elsewhere, Wolfsburg moved closer to saftey with a 3-0 home win over Darmstadt while Werder Bremen were held 2-2 at home to Borussia Moenchengladbach.
Two goals from Nick Woltemade saw Bremen come from behind after Robin Hack's early opener for Gladbach, but the visitors snatched a point when Florian Neuhaus smashed a late penalty into the top corner.
Two early goals from Patrick Wimmer and Jonas Wind and a late strike from Vaclav Cerny saw Wolfsburg cruise past already relegated Darmstadt.
Ralph Hasenhuettl's side are now nine points clear of the relegation play-off place, having played one more game than fellow strugglers Mainz.