Bayern Munich were crowned Bundesliga champions on Tuesday for an eighth straight season as Robert Lewandowski's volley secured a 1-0 win at Werder Bremen, while Paderborn were relegated from the top flight in Berlin.
Bayern picked up their eighth consecutive win since the Bundesliga resumed in mid-May behind closed doors due to the coronavirus, as coach Hansi Flick won the league title in his first season in charge.
"Compliments to the team, it is sensational what we have achieved in the past few months," said Flick whose side have won all of their last 14 games.
"Today there is no criticism, you have to emphasise the way the players have done it.
"Player and coach, team have simply been one unit."
A deft chip over the Bremen defence from Jerome Boateng was chested down and volleyed home by Lewandowski, who claimed his 31st league goal this season and his 46th in all competitions, shortly before half-time.
But Bayern endured a nervy finale after teenage left-back Alphonso Davies was sent off 11 minutes before the final whistle for a second yellow card.
He was lucky to avoid a straight red after a kick on Leonardo Bittencourt which earned him his first yellow on 19 minutes.
The result keeps Werder Bremen second-from-bottom with just two games left to avoid dropping down to the second-tier for the first time since 1980.
Bottom side Paderborn had their relegation confirmed with a 1-0 defeat at Union Berlin after an own goal from the visitors by Ben Zolinski.
"There was always a little bit missing in our game", said Paderborn captain Christian Strohdiek.
"When the disappointment fades, we can simply be proud of what we have achieved in the last few years," added Strohdiek after Paderborn had earned back-to-back promotions in the previous seasons.
Union's win in Berlin means they are guaranteed a second Bundesliga season having come up for the first time in 2018/19.
Seventh-placed Freiburg stayed in the hunt for a Europa League place next season after replacement striker Nils Petersen came off the bench to net the winning goal and seal a 2-1 win at home to Hertha Berlin.
It was Petersen's 11th goal of the season, but the 25th of his career which he has scored as a substitute.
- Gladbach hunt Champions League -
Earlier, Borussia Moenchengladbach stayed in the hunt for a Champions League berth with an emphatic 3-0 home win over Wolfsburg as midfielder Jonas Hofmann scored twice.
After consecutive defeats by Freiburg and Bayern, Gladbach raced into a two-goal lead after half an hour at Borussia Park.
Hofmann scored twice before Germany international Lars Stindl swept a third into the net following a second-half counter-attack.
"We scored three goals, didn't concede and picked up three points with an ambitious performance in difficult conditions, so I am happy with that," said Gladbach head coach Marco Rose.
The result was all the more impressive as Gladbach eased to victory without injured French forwards Marcus Thuram and Alassane Plea.
Gladbach moved back into the fourth and final Champions League spot, two points ahead of Bayer Leverkusen, who host Cologne on Wednesday in their game in hand.
Bayern and Borussia Dortmund have already qualified for next season's group stage, while RB Leipzig sit third, five points clear of Leverkusen.
The defeat leaves Wolfsburg sixth, which carries a Europa League place next season.
Gladbach face Paderborn on Saturday, then mid-table Hertha Berlin on the final day of the season, while Leverkusen face Hertha and Mainz in their last two games.
Robert Lewandowski (L) chests the ball down before volleying the winner
Ex-Dortmund midfielder Jonas Hofmann scored twice