Luca Waldschmidt's late winner condemned Wolfsburg to Bundesliga's relegation play-off as Hamburg survived on the final day.
Arjen Robben scored deep into stoppage time as Bundesliga champions Bayern Munich twice battled back to clinch a spectacular 5-4 victory over RB Leipzig.
Bayern Munich secured their fifth consecutive Bundesliga title with a 6-0 rout of Wolfsburg on Saturday.
Guido Burgstaller scored twice as Schalke jumped up to eighth place in the Bundesliga table with a comprehensive 4-1 away win at Bayer Leverkusen.
RB Leipzig failed to grasp a chance to close the gap on Bundesliga leaders Bayern Munich as they were held to a 1-1 draw at Schalke.
Ajax reached their first European semi-final in 20 years after beating Schalke 4-3 on aggregate in the Europa League after extra-time.