Robert Lewandowski scored an 85th-minute winner from the spot as Barcelona snatched a 2-1 LaLiga victory at 10-man Osasuna on Sunday.
The Spanish champions were outplayed for large spells of the game at El Sadar but Jules Kounde put them ahead in first-half injury time.
Chimy Avila looked to have rescued a deserved point for the hosts after 76 minutes but Alejandro Catena was sent off for pulling back Lewandowski in the box and the Pole scored the resulting penalty.
Elsewhere, Portu scored in the 88th minute to hand Girona a 1-0 win over Las Palmas that leaves them second, two points behind Real Madrid, while Mallorca and Athletic Bilbao played out a goalless draw.
Kylian Mbappe scored twice as French champions Paris St Germain powered to a 4-1 win over troubled Lyon in Ligue 1.
Achraf Hakimi and Marco Asensio also got on the scoresheet at the Groupama Stadium as PSG piled on the misery for under-fire home manager Laurent Blanc.
The result left Lyon bottom of the table with just one point from four games.
They were overtaken by Clermont, who claimed their first point of the season by fighting back from 2-0 down to snatch a last-gasp 2-2 draw against Toulouse. Florent Ogier scored their injury-time equaliser.
Metz and Reims also drew 2-2 while Le Havre overpowered Lorient 3-0, Lille edged out Montpellier 1-0 and Nice saw off Strasbourg 2-0.
Lautaro Martinez struck twice as Inter Milan moved to the top of Serie A with an emphatic 4-0 win over Fiorentina at San Siro.
Marcus Thuram and Hakan Calhanoglu, with a penalty, also got on the scoresheet as Inter maintained their 100 per cent start to the campaign.
Juventus continued their unbeaten start with a 2-0 triumph at Empoli. Danilo and Federico Chiesa scored in each half.
Nemanja Radonjic scored a stoppage-time winner as Torino beat Genoa 1-0 and Lecce beat Salernitana 2-0.
In Germany, Benjamin Sesko scored twice in the last five minutes to wrap up a 3-0 win for RB Leipzig over 10-man Union Berlin.
Xavi Simons had opened the scoring after 51 minutes and Union’s hopes of getting back into the game were hit when Kevin Volland was sent off just after the hour.
Niels Nkounkou struck in the 87th minute to cancel out a penalty from Florian Kainz and earn Eintracht Frankfurt a 1-1 draw at home to Cologne.
Hoffenheim 4-2 Bayern Munich: Tuchel bows out on defeat thanks to Kramaric hat-trick
Bayern Munich squandered a two-goal lead to slump to a 4-2 loss at Hoffenheim courtesy of a second-half Andrej Kramaric hat-trick in Thomas Tuchel's final game.
Early goals from Mathys Tel and Alphonso Davies saw the injury-depleted Bavarians go 2-0 up by the sixth minute.
Hoffenheim, however, pulled a goal back through Germany international Maximilian Beier just two minutes later, with the hosts gradually taking some of the early pace out of the game.
Bayern's injury troubles were further compounded when they lost Aleksandar Pavlovic to injury in the 35th minute, and struggled to cope with Hoffenheim's threat in the second half.
Kramaric then delivered a stunning 19-minute hat-trick with the Bayern defence in ruins, ending a disappointing season in third place with 72 points.
Bayer Leverkusen finished in top spot on 90 points. VfB Stuttgart finished runners-up on 73 with a 4-0 demolition of Borussia Moenchengladbach, while Hoffenheim finished seventh, in the Europa Conference League place.
Data Debrief:
Thomas Muller made his 473rd Bundesliga appearance for Bayern on Saturday, drawing level with Sepp Maier as the club's record appearance maker in the competition.
Bayern failed to have a single shot on target in the second half, while Kramaric ran riot to subject Bayern to their worst league finish since 2011.
Bayer Leverkusen 2-1 Augsburg: Bundesliga champions make history with unbeaten season
Bayer Leverkusen became the first team in Bundesliga history to complete a full season unbeaten after beating Augsburg 2-1 on the final day.
Xabi Alonso's treble-chasing team also stretched their European record unbeaten run across all competitions this season to 51 matches.
Victor Boniface intercepted a ball from Augsburg keeper Tomas Koubek to tap in for the lead in the 12th minute before Robert Andrich, part of Germany's Euro 2024 preliminary squad, doubled the advantage from close range.
Augsburg cut the deficit when Mert Komur scored just after the hour.
Leverkusen captain Lukas Hradecky made a smart stop to maintain Leverkusen's clean sheet, as the Bundesliga champions held on to make history.
Alonso's team, who face Atalanta in the Europa League final on Wednesday and also take on Kaiserslautern in the DFB-Pokal final on May 25, finished on 90 points, 17 ahead of second-placed Stuttgart and 18 ahead of Bayern Munich, who lost 4-2 at Hoffenheim.
Data Debrief: Leverkusen's remarkable run rolls on
What an incredible season it has been for Leverkusen, and Alonso's men are now just two wins away from unprecedented success.
Leverkusen have become only the second team in Bundesliga history to not lose a single point from winning positions in a season, matching a feat Bayern managed in 2011-12.
They have won 45 points (W13 D3) in their 17 home games in the Bundesliga this season and have remained unbeaten at home for only the second time, after 1999-2000.
Leverkusen are the second club in league history to reach the 90-point mark, following Bayern (90 points in 2013-14 and 91 points in 2012-13).
Guirassy matches Kiessling, Muller record with another opener
Stuttgart's Serhou Guirassy matched a Bundesliga record previously shared by Stefan Kiessling, Ailton and Gert Muller with his opener against Borussia Monchengladbach.
Guirassy put high-flying Stuttgart ahead in the 23rd minute on Saturday, in their final game of the season.
That goal marked the 12th time the striker has scored the opener in a Bundesliga match this season, which equalled the record set by the great Muller in 1969-70, then matched by Ailton in 2003-04 and Kiessling in 2012-13.
It also brought up Guirassy's 27th goal of a stellar campaign.
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