Vincent Kompany's men were made to work hard for their eighth straight league victory, eventually breaking down a stubborn Monchengladbach side with three goals in 17 minutes after the interval.

The hosts were reduced to 10 men early on when Jens Castrop was sent off after just 18 minutes, yet they defended resolutely until Joshua Kimmich finally broke the deadlock with his first goal of the season.

Raphaël Guerreiro soon added a second, and Lennart Karl sealed the result with his maiden Bundesliga goal - just days after scoring his first senior goal for the club.

"In the first half there were a lot of emotions. Gladbach fought for every ball, and even after the red card you could feel they were giving everything. We stayed calm, kept our tempo high in the second half, and at some point, you simply have to take your chance, that is exactly what we did," said Kompany.

Elsewhere, Borussia Dortmund claimed a dramatic 1-0 win over Köln thanks to a stoppage-time strike from substitute Maximilian Beier. The match appeared destined for a draw at Signal Iduna Park until Beier calmly slotted home in the 96th minute to seal all three points for the hosts.

Köln had the best chance of the first half when Said El Mala missed a golden opportunity with only Gregor Kobel to beat, while Dortmund's Serhou Guirassy squandered a close-range effort early in the second half. Despite creating more chances, including efforts from Felix Nmecha and Julian Brandt, Dortmund were repeatedly denied by Marvin Schwäbe in the Köln goal.

Persistence ultimately paid off in the dying moments, as Fabio Silva teed up Beier to deliver a dramatic late winner — sparking relief and celebration among the home fans after a hard-fought contest.

Dortmund's coach Niko Kovac praised his team's mentality after their late win.

"You really have to say that Köln did really well," he said. "They defended very well. We pressed up from the first minute, and we defended high. That put our opponents to stay inside their half until the end. That's what I want, and that's what our fans want to see."

RB Leipzig produced a ruthless display to crush Augsburg 6-0, matching their second-biggest Bundesliga victory ever and tightening their grip as Bayern's nearest title challengers in second place on the table.

Ole Werner's side were clinical from the outset, scoring four times before halftime in a dazzling attacking performance that left the visitors shell-shocked.

Yan Diomande opened the scoring after just 10 minutes with a superb solo effort before Romulo doubled the lead from an Assan Ouedraogo assist. Leipzig continued to punish Augsburg on the counter, with Antonio Nusa and Christoph Baumgartner adding two more goals before the break. Despite some attacking intent from Augsburg, their lack of composure in the final third and shaky defending repeatedly left them exposed.

The second half brought little relief for the struggling hosts. Ouedraogo added a fifth with a precise strike following a neat exchange with Baumgartner, while Castello Lukeba completed the rout after poor goalkeeping from Finn Dahmen. The emphatic win extended Leipzig's unbeaten run to seven league matches, while Augsburg - now holding the league's worst defensive record - face growing fears of a relegation battle.

Friday and Saturday Bundesliga Results

Werder 1-0 Union Berlin

Eintracht Frankfurt 2-0 FC St. Paul

Augsburg 0-6 RB Leipzig

Hamburger SV 0-1 Wolfsburg

Hoffenheim 3-1 Heidenheim

Monchengladbach 0-3 Bayern

Borussia Dortmund 1-0 Köln

Borussia Dortmund back Julian Brandt to stay amid contract talks