Borussia Dortmund slipped up in their chase for third spot as Hoffenheim hammered Werder Bremen to go level on points.
Dortmund were held 1-1 by Augsburg, who picked up a valuable point in their battle against relegation, after Pierre-Emerick Aubameyang equalised Alfred Finnbogason's opening goal. Julian Weigl was also taken off early, and the team confirmed he suffered a broken ankle.
However, Hoffenheim's 5-3 win over Bremen -- with goals from Adam Szalai, Andrej Kramaric (2), Steven Zuber and Ermin Bicakcic -- saw them move level on 61 points, but four behind on goal difference.
The third-placed team will earn a spot in the Champions League group stage, while fourth must go through the playoff round.
Arjen Robben scored deep into stoppage time as Bundesliga champions Bayern Munich twice battled back from two goals down to clinch a spectacular 5-4 victory over ambitious RB Leipzig.
The hosts, who will finish a distant second behind Bayern, were ahead as early as the second minute through Marcel Sabitzer, and although Robert Lewandowski equalised, further strikes from Timo Werner -- from the penalty spot -- and Yussuf Poulsen appeared to have put Leipzig in control.
Thiago closed the gap to a single goal once more before Werner's second made it 4-2 to the hosts.
Late drama followed, however, with Lewandowski reducing the deficit once more and David Alaba levelling things up in the first minute of stoppage time before Robben's left-footed strike five minutes later snatched an unlikely win and ensured Bayern sit 13 points clear of their rivals with one game left.
Down at the other end of the table Ingolstadt's two-year stay in the Bundesliga is over after a 1-1 draw against Freiburg condemned the Bavarians to relegation.
Maximilian Philipp gave Europa League hopefuls Freiburg the lead on 31 minutes before Dario Lezcano headed in an equaliser just before the break. However, Hamburg's last-gasp 1-1 draw at Schalke leaves Ingolstadt four points adrift of safety heading into the final weekend.
Hamburg still have work to do to avoid a first-ever relegation from the Bundesliga despite Pierre-Michel Lasogga's goal in stoppage time.
Die Rothosen have not been demoted from the German top flight since the Bundesliga's inception in 1963 but they are now two points adrift in the relegation playoff place. Guido Burgstaller's first-half goal for Schalke had left them all-but guaranteed to finish 16th but Lasogga's equaliser gives them hope of catching either Mainz, Augsburg or Wolfsburg -- whom they face on the final day.
Mainz did their chances no harm by coming from behind to beat Eintracht Frankfurt 4-2.
Goals either side of half-time from Branimir Hrgota and Haris Seferovic looked like handing Frankfurt victory but Jhon Cordoba, Stefan Bell, Yoshinori Muto and Pablo de Blasis all struck in the final half-hour for Mainz.
Elsewhere, Borussia Monchengladbach drew 1-1 with Wolfsburg, Bayer Leverkusen fought back to draw 2-2 against Cologne and already-relegated Darmstadt lost 2-0 at home to Hertha Berlin.