Harry Kane scored his 36th goal of the Bundesliga season but second-placed Bayern Munich lost 3-1 at VfB Stuttgart in third on Saturday, while Wolfsburg are all but safe after a 3-0 win over already relegated Darmstadt.
Borussia Mönchengladbach nudged five points above the relegation play-off spot after grabbing a late 2-2 draw at 10th-placed Werder Bremen.
Yousouffa Moukoko twice, Donyell Malen, the departing Marco Reus and Felix Nmecha struck as Borussia Dortmund won 5-1 at home to Augsburg - despite resting most of their top names ahead of the Champions League semi-final second leg with Paris-Saint Germain on Tuesday.
Fifth-placed Dortmund have already sealed a place in the extended Champions League next season, along with Bayern, Stuttgart, RB Leipzig and champions Bayer Leverkusen, after German sides' success in Europe offered up an extra spot.
Bayern could though suffer the ignominy of finishing third behind Stuttgart after the surprise packages of the season moved just two points behind the Bavarians with two to play thanks to Jeong Woo Yeong's 83rd-minute header and Silas Katompa Mvumpa in stoppage time.
Leonidas Stergiou had netted the opener before Kane's penalty.
Second-bottom Cologne host Europa League-chasing Freiburg in Saturday's late game desperate for a win to give themselves hope of avoiding the drop. If they lose and third-bottom Mainz win at Heidenheim on Sunday, Cologne are down.
