While Bayern were squeezing past bottom club Paderborn, Leipzig were shocked 3-1 at home to Schalke to surrender top spot.
Defending champions Bayern took full advantage to top the Bundesliga table before Tuesday’s key Champions League clash at Tottenham Hotspur, but not before Paderborn gave them a scare.
“We didn’t really finish them off,” admitted Serge Gnabry, who netted Bayern’s first goal.
“We had a lot of chances to decide the game, but our finishing let us down.
“It will be totally different against Spurs — we have to raise our game.”
Coutinho, who is rebooting his career on loan in Munich after an unhappy stint at Barcelona, played a key role by setting up Gnabry’s opening goal with a sublime first-half pass.
Having scored his first Bayern goal the week before in a rout of Cologne, the Brazilian playmaker tapped home Gnabry’s neat pass after the break before substitute Kai Proeger pulled a goal back for Paderborn.
With time almost up, Lewandowski showed great finishing prowess to put away a Niklas Suele pass and make it 3-1, becoming the first Bayern player to score in each of the first six matches of the season.
He is also the first Bundesliga player to reach 10 goals after the first six games.
However, there were nervous looks in Bayern’s ranks during the final ten minutes after Paderborn defender Jamilu Collins beat Germany goalkeeper Manuel Neuer from 30 metres out late on.
Harit downs Schalke
In Leipzig, Morocco international midfielder Amine Harit inspired Schalke to an impressive away win, winning and drilling home a penalty and setting up a first Bundesliga goal for Welsh teenager Rabbi Matondo.
The Royal Blues raced into a 2-0 lead with first-half goals as Senegalese centre-back Salif Sane headed home from a corner on 29 minutes, then Harit drilled home a penalty just before the break.
The referee took a long look at the replays after Harit went down after the faintest of contact from Mali defender Amadou Haidara. Harit slammed home the spot kick.
Schalke, under ex-Huddersfield coach David Wagner, made sure of the three points when Matondo claimed his first Bundesliga goal since joining from Manchester City.
Harit again did the damage, punishing a mistake in midfield then putting in a well-timed pass which sent Liverpool-born Matondo away to fire home on 58 minutes.
Emil Forsberg’s consolation goal came too late for Leipzig.
The shock result shook up the table as Bayern climbed top, Schalke leaped from fifth to second and Leipzig dropped to third.
Borussia Dortmund must win at home to Werder Bremen later to lift them from seventh.
Borussia Moenchengladbach went fourth as goals from French strikers Alassane Plea and Marcus Thuram sealed a 2-0 victory at Hoffenheim.
Bayer Leverkusen are just behind them in fifth thanks to late goals from forwards Kevin Volland and Kai Havertz that added to a Florian Niederlechner’s first-half own goal in a 3-0 win at Augsburg.
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