Bayern Munich stretched their lead in the Bundesliga to 11 points following a crushing 6-0 win at Paderborn on Saturday, while Augsburg goalkeeper Marwin Hitz scored a stoppage-time equaliser against Bayer Leverkusen.
Bayern were held scoreless by Shakhtar Donetsk in the Champions League on Tuesday but the title holders have now scored 14 goals in two league matches.
Robert Lewandowksi's first-half double on his return to the starting line-up got Bayern on their way, while Arjen Robben is now the league's top scorer after getting his 15th and 16th goals of the season.
Franck Ribery and Mitchell Weiser also netted as Bayern scored four times in the second half after the home team had Florian Hartherz sent off.
Visiting manager Pep Guardiola was satisfied with the performance, although he also indicated that the game was tougher than the scoreline suggested.
"We played with great seriousness and hardly gave up any chances," the Bayern coach said.
"It was hard to play against their five-man defence. I said beforehand that Paderborn will stay in the Bundesliga. Now I'm certain of it."
Lewandowski beat home 'keeper Lukas Kruse from Robben's pass on 24 minutes and the Polish striker got his 10th league goal of the season eight minutes before half-time when he turned home Ribery's low centre.
Any hope of a fightback by the home side disappeared when Hartherz was red carded on 63 minutes after colliding with Robben. The Dutch winger picked himself up to convert from the penalty spot.
Ribery fired home from inside the box with 18 minutes left before substitute Weiser made it five with a clever lob over Kruse.
Robben completed the scoring from another Ribery cross.
- 'Keeper Hitz rescues Augsburg –
Meanwhile, there was late drama in Augsburg as goalkeeper Hitz stabbed home in the fourth minute of injury time to salvage a 2-2 draw against Leverkusen.
Josip Drmic's eighth-minute goal gave Leverkusen a deserved lead but Brazilian attacker Caiuby poked home his first goal for Augsburg after 59 minutes.
A deflected shot from Stefan Reinartz looked to have won it for Leverkusen but they failed to clear a corner and Hitz volleyed in from close range.
He becomes the first goalkeeper to score a Bundesliga goal from open play since Frank Rost for Werder Bremen in March 2002.
There was still time for Augsburg's Halil Altintop to hit the post but they stay fifth ahead of Leverkusen.
"Football writes such stories," Augsburg manager Markus Weinzierl said. "Marwin Hitz was standing in the perfect spot.
"It doesn't bear thinking about what would have happened if Halil Altintop had scored too. That would have been too much of a good thing."
Meanwhile, Bremen are still unbeaten in 2015 after Sebastian Proedl got an injury-time equaliser for a 1-1 draw at fourth-placed Schalke.
Werder, who started the day in eighth, had been looking for a sixth league win in succession. But they fell behind on 61 minutes when Max Meyer's weak effort was spilled into the corner by goalkeeper Raphael Wolf.
However, Proedl nodded home from a free-kick two minutes into stoppage time.
Elsewhere, Martin Schmidt's reign as manager of Mainz 05 got off to a dream start as they came from behind to beat Eintracht Frankfurt 3-1 in the Rhine-Main derby.
In the evening game, Nigerian striker Anthony Ujah scored Cologne's first goal at home in 363 minutes of football as they hit back for a share of the points against Hanover.
Third-bottom Freiburg also drew 1-1 at home to mid-table Hoffenheim after a thumping strike from Kevin Volland cancelled out Immanuel Hoehn's goal.
On Friday, goals from Pierre-Emerick Aubameyang, Ilkay Gundogan and Marco Reus saw Borussia Dortmund warm up for their Champions League clash with Juventus by winning 3-2 at bottom club VfB Stuttgart.
Dortmund are now seven points clear of Stuttgart following their third league win in a row.
Source: AFP