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 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 opened the scoring before Kane's penalty.
"We're simply relieved. We have worked the whole year for this," Stuttgart midfielder Angelo Stiller told Sky.
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.
With one eye on Wednesday's Champions League semi-final second leg at Real Madrid (2-2), outgoing Bayern coach Thomas Tuchel made six changes given there is little left to play for domestically.
Winger Serge Gnabry, who is regaining match sharpness, started but Jamal Musiala, Leon Goretzka, Leroy Sané, Thomas Müller, Konrad Laimer and Noussair Mazraoui were all rested. Raphael Guerreiro was in the line-up but had limp off in the first half.
"We are cursed. Bitter, bitter, bitter," said Tuchel.
Kane also started as he still has an outside chance of beating Robert Lewandowski's record of 41 goals in a Bundesliga season.
But Stergiou scored his first of the season on the half hour, with Bayern's Eric Dier off the pitch having a head wound patched up.
England striker Kane did get on the scoresheet by half-time when he converted a penalty after Gnabry was caught by Waldemar Anton's arm.
Stuttgart have performed wonders having almost gone down last term and a late flurry secured a first home win over Bayern since 2007.
Dortmund's Edin Terzic, whose side take a 1-0 lead to Paris, rotated 10 players against Augsburg with a Champions League spot safe.
Reus, who scored the fourth, was one of those to come into the team having announced on Friday that he will leave the club in June.
He received a huge reception by fans and said: "It's been indescribable, you can't beat it. I am so grateful. I will play on."
Germany could yet have six spots in next season's premier club competition if Bayern or Dortmund win this term's Champions League.
The Europa League and Europa Conference League places via the Bundesliga are also linked to Bayern or Dortmund's Champions League fortunes, plus whether champions Leverkusen also win the German Cup.
Ninth-placed Augsburg's loss hit the chances of Jess Thorup's side.
On Friday, Hoffenheim moved up to seventh, the current qualification spot for the Conference League, after Andrej Kramaric scored a late goal to secure a 1-1 draw with Leipzig in fourth.
On Sunday, Union welcome Bochum with neither side safe. Both are just two points ahead of Mainz, who occupy the relegation play-off spot. Champions Leverkusen go to sixth-placed Eintracht Frankfurt.
