The Gunners dominated the second half after Bayern's 17-year-old midfielder Lennart Karl cancelled out Jurrien Timber's opener in the opening period.

Noni Madueke opened his goalscoring account for the Premier League frontrunners to restore their lead and fellow substitute Gabriel Martinelli took advantage of a huge blunder from goalkeeper Manuel Neuer.

England captain Harry Kane, a former Tottenham player, had a miserable return to London, largely a peripheral figure despite his astonishing goalscoring record for the six-time European champions.

"Look at Bayern Munich this season, they have been the best team in Europe," Arsenal midfielder Declan Rice told TNT Sports.

"This was probably the toughest game tactically we have played this season. The way they work it is so, so good."

The England man said this season feels different from the previous campaign, when Arsenal again came up short, finishing second in the Premier League for a third straight season.

"There are so many leaders in the team," Rice added. "We are just taking it one game at a time. There is a hunger and desire to win every game. There is a long way to go -- let's not get carried away."

Bayern started the match at the Emirates top of the Champions League table, just above the Gunners, with both teams having won four games out of four.

- Set-piece brilliance -

The game took time to come alive but the Gunners went ahead in the 22nd minute when Timber headed home a Bukayo Saka corner, with a flailing Neuer unable to intercept.

The goal underlined Arsenal's relentless brilliance from set-pieces.

Eberechi Eze, who scored a hat-trick in Sunday's 4-1 win against Tottenham, had a glorious chance to double the Gunners' lead but scuffed his shot wide.

Arsenal had looked relatively comfortable but Bayern were back in the game in the blink of an eye in the 32nd minute, courtesy of Karl's goal.

Joshua Kimmich played a superb diagonal ball that was laid off first time by former Arsenal player Serge Gnabry and Karl finished confidently past David Raya.

Arsenal were quickly on the front foot in the second half, with Neuer pushing a fierce Saka shot over the bar.

Karl then surged down the right and into the home side's penalty box but his weak shot was easily collected by Raya.

As the intensity built, Arsenal's Mikel Merino failed to connect properly with another dangerous corner before Neuer saved a Cristhian Mosquera header from point-blank range.

Now it was all Arsenal.

Neuer was called into action again, saving with his legs as Rice bore down on him, with Saka unable to turn in the loose ball.

But the pressure finally paid off with just over 20 minutes to go, when Bayern defender Dayot Upamecano played a stray ball that was picked up by substitute Riccardo Calafiori on the left.

He crossed and fellow substitute Madueke turned the ball home.

There was worse to come for Bayern when Eze sent a long ball over the top, with Neuer well outside his area.

Martinelli's first touch took him past the stranded goalkeeper and he had a free run at goal, maintaining his nerve to slot home.

The delirious Arsenal fans taunted Kane, with a chant of "Harry, Harry, what's the score" as they revelled in his misery.