Going into the game without talismanic striker and Bundesliga top scorer Harry Kane, who was suspended for the encounter, the Bavarians struggled up front in the first half.
As a result, the home side was able to take a surprise, but well-deserved on the balance of play, 2-0 lead into the break thanks to goals from Benjamin Sesko (11') and Lukas Klostermann (39').
Bayern were much better after the break, though, and managed to claw their way back into the game thanks to two goals in less than a minute from Eric Dier (62') and Michael Olise (63') to draw level.
The Bundesliga leaders thought they had secured the title when Leroy Sane struck in the 83rd minute and there were even pictures of Kane on the sideline ready to rush onto the field to celebrate.
However, Yussuf Poulsen had other ideas and broke Bavarian hearts all over the world when he saved a point for Leipzig with a goal deep into stoppage time.
There were plenty of goals without many wins in elsewhere in the Bundesliga on Saturday too, with Borussia Monchengladbach and Hoffenheim playing out to a thrilling 4-4 draw.
Fabio Chiarodia (5') and Rocco Reitz (32') got Gladbach off to a fast start before goals from Arthur Chaves (43') and Marius Bulter (54') on either side of halftime restored parity.
Monchengladbach retook the lead through Franck Honorat in the 64th minute but it only last nine minutes until Adam Hlozek made it 3-3 in the 73rd minute.
Hoffenheim looked to have stolen the points when Haris Tabakovic scored in the 81st minute but Tim Kleindienst had other ideas and rescued a point for Gladbach in stoppage time.
Union Berlin and Werder Bremen drew 2-2 in the third high-scoring draw of the day, while the outlier was the 0-0 draw between Heidenheim and Bochum.
Nick Woltemade's 88th-minute strike was enough to secure a 1-0 win for Stuttgart over 10-man St Pauli.
Bayern Munich chief Uli Hoeness has insisted the club's transfer window was a success, even though they were unable to secure the signing of German international Florian Wirtz.
Thomas Tuchel has expressed full confidence in Harry Kane as England prepare for a key 2026 World Cup qualifier against Serbia in Belgrade on Tuesday.
Bayern Munich's honorary president has firmly dismissed the possibility of Nicolas Jackson making a permanent move from Chelsea, stating there's no way the striker will fulfill the required conditions for the transfer.
Bayern Munich's honorary president Uli Hoenes has been hyper cricital of Newcastle United's spending in the recently concluded transfer window, especially in regards to their purchase of Nick Woltemade from Stuttgart.
