BERLIN - Stuttgart was relegated on the final day of the Bundesliga after losing at Wolfsburg 3-1, while Werder Bremen clinched survival with a late 1-0 win over Eintracht Frankfurt on Saturday.

Papy Djilobodji prodded the ball over the line after a goalmouth scramble in the 88th minute for Bremen to overtake Frankfurt.

Now Frankfurt faces a two-leg playoff against Nuremberg — third in the second division — to determine which side plays top-tier football next season.

"The team will have to show another face on Thursday," Frankfurt coach Niko Kovac said of the first leg in Frankfurt.

Stuttgart, which finished three points below Frankfurt, joined already-relegated Hannover in the second tier.

"We were relegated in the last weeks, not today. Today we just got the receipt," Stuttgart coach Juergen Kramny said after the side's sixth consecutive defeat.

Bremen, which started the day in the relegation playoff place, climbed to 13th and safety, sparking jubilation among relieved fans.

"As a player I experienced the title win in 2004. That was also attractive of course. But what's happening here now is unbelievable," Bremen coach Viktor Skripnik said.

Mario Goetze scored twice as Bayern Munich kicked off its title celebrations with a 3-1 win over Hannover. Bayern, which secured an unprecedented fourth successive title in Ingolstadt the weekend before, finished the season with 88 points, 10 more than second-placed Borussia Dortmund.

"We also really celebrated after Ingolstadt. Some of us kept it going very long. We'll see if we can top it today," Bayern captain Philipp Lahm said.

Marco Reus' 75th-minute free kick salvaged a 2-2 draw for Dortmund against Cologne, maintaining the side's unbeaten record at home all season.

Dortmund coach Thomas Tuchel was upset, however, that the side failed to win its last two games.

"It's a pity that we ended the season after 32 games," said Tuchel, who said his team has lost form at the wrong time. Dortmund plays Bayern in the German Cup final in Berlin next Saturday.

"I'm very worried about our ability to compete ... it's self-inflicted," Tuchel said.

Schalke won at Hoffenheim 4-1 to move to fifth, overtaking Mainz and Hertha Berlin after their goalless draw, and securing automatic qualification for the Europa League, along with Mainz. Hertha, which finished seventh, has to go through the qualification process. Niklas Stark was sent off late for Hertha.

Klaas Jan Huntelaar, Eric Maxim Choupo-Moting and Leroy Sane scored for Schalke, before a late own goal from Fabian Schaer completed the scoring.

Schalke coach Andre Breitenreiter said before the game that it would be his last in charge after being told by incoming general manager Christian Heidel that he was being let go halfway into his two-year contract.

Bayer Leverkusen, already assured of third place, came from behind to beat Ingolstadt 3-2 at home.

American goalkeeper David Yelldell came on in the second half to make his Bundesliga debut after nearly five years at Leverkusen, but he couldn't prevent Moritz Hartmann from scoring Ingolstadt's consolation with a penalty.

Borussia Moenchengladbach finished fourth, three points above Schalke, thanks to a 2-0 win at Darmstadt with goals in either half from Thorgan Hazard and Andre Hahn, for a spot in the Champions League qualifying round.

"We always believed that we could still reach the Champions League," said Hahn, whose side endured a poor start to the season until Andre Schubert took over as coach.

Michael Gregoritsch scored twice as Hamburger SV came from behind to win 3-1 at Augsburg, whose coach Markus Weinzierl is tipped to take over at Schalke. Hamburg finished 10th, two places ahead of Augsburg.

Stuttgart needed to beat Wolfsburg and hope for a big-scoring win from either Bremen or Frankfurt to salvage the relegation-promotion playoff, but their hopes were ended when Maximilian Arnold and Andre Schuerrle put Wolfsburg 2-0 ahead in less than half an hour.

Martin Harnik struck the crossbar for luckless Stuttgart before Daniel Didavi scored late against his future side. Schuerrle then claimed his second in the last minute for Wolfsburg, which finished eighth after a disappointing season.

Bundesliga top-scorer Robert Lewandowski got Bayern's party underway with his 30th goal of the season against Hannover, a deflected effort in the 12th minute.

World Cup winner Goetze made it 2-0 with a fine chip over the goalkeeper 16 minutes later and then claimed only his third goal in a disappointing season for the player after a corner in the 54th.

Goetze hadn't scored since Bayern's 5-1 win over former club Dortmund in October.

Artur Sobiech scored Hannover's consolation before Bayern's players could celebrate the title with the customary beer showers.

"It was cold, so cold," Bayern coach Pep Guardiola said after being doused in beer again after his last game in Munich. The Spanish coach, who is leaving for Manchester City next season, won the title in each of his three years in charge.