After a dominant opening half in which Thomas Muller hit the crossbar, the Bundesliga leaders – facing Chelsea for the first time since losing to the Blues in the 2012 final – took the match away from their hosts in the space of three second-half minutes.
Gnabry, who scored four in a 7-2 rout over Tottenham in Bayern's last trip to London, netted a brace when twice combining brilliantly with Robert Lewandowski, who got Bayern's third with 14 minutes remaining.
With Bayern in the ascendency ahead of the return fixture on home soil, Chelsea's misery was compounded when Marcos Alonso was sent off late on.
6 - Serge Gnabry is the first player in Champions League history to score each of his first six goals in the competition all against sides from the same nation (4 v Tottenham, 2 v Chelsea). Gunner. #CHEBAY pic.twitter.com/FwfXanlclq— OptaJoe (@OptaJoe) February 25, 2020
Retaining his place in Chelsea's line up at Kepa Arrizabalaga's expense, Willy Caballero had a save to make in the first minute when he kept out Muller's strike.
Muller turned provider 10 minutes later with a brilliant exchange of passes with Kingsley Coman, who sliced wide, while Caballero twice denied Lewandowski.
With Olivier Giroud failing to turn in Mason Mount's cross at the other end, the bar came to Chelsea's rescue from a Muller header.
But Bayern made no mistake with their next chance – Lewandowski squaring for the supporting Gnabry to side-foot home.
They swiftly added a second, too, with Lewandowski and Gnabry combining once more for the latter to slot into the bottom-right corner.
Gnabry could have had his third before the hour only to hammer over on the volley, though Bayern were inconvenienced by Coman succumbing to an apparent hamstring injury.
Chelsea seemed to be gathering a head of steam late on, yet Frank Lampard's side found themselves down – and all but out – when the excellent Alphonso Davies raced clear to tee up Lewandowski for his 11th Champions League goal of the season, with Alonso then seeing red after a VAR check for violent conduct.
What does it mean? Premier League must be the priority for Chelsea
Bayern have dropped Bundesliga points just once – against RB Leipzig – since November at home. Having scored three away goals, they have a comfortable cushion which should be easily enough to see them go through to the last eight.
For Chelsea, however, the target now must be ensuring they shake off competition from Tottenham and Manchester United – along with a host of other clubs – to finish within the Champions League qualification spots in England's top tier.
London calling for ex-Gunner Gnabry
Gnabry – a former Arsenal player – has now scored six goals in the Champions League this season, with all of them coming in the English capital. He displayed brilliant composure for his opener and unerring accuracy with his second.
Reckless Alonso falls foul of VAR
As if things were not already going to be difficult enough in the second leg, Chelsea will be without one of their most experienced players after Alonso got himself sent off for lashing out at Lewandowski off the ball. A VAR check led to the colour of the card shown to the defender changing from yellow to red.
4 - Bayern Munich have now scored 3+ goals away from home at four separate English clubs in the Champions League - Arsenal (twice), Manchester City, Tottenham Hotspur and Chelsea - with each instance coming since 2013. Bullying. #CHEBAY pic.twitter.com/Ux5AHU0Yyw— OptaJoe (@OptaJoe) February 25, 2020
Key Opta facts
- Chelsea have suffered eight home defeats in all competitions this season, their worst tally of home defeats since the 1985-86 season (also eight).
- Bayern are only the third team in Champions League history to win their first seven games in a season, after Barcelona in 2002-03 and Real Madrid 2014-15, neither of whom went on to win the trophy.
- This was Chelsea's heaviest ever home European defeat and their heaviest defeat at Stamford Bridge in any competition since January 2018 (3-0 v Bournemouth in the Premier League).
- Serge Gnabry has scored six goals in two appearances in London for Bayern Munich, having scored none in nine appearances in London for Arsenal between 2012 and 2014.
- Hansi Flick became only the seventh manager to win his first four Champions League matches, and the first since Diego Simeone in November 2013.
- Marcos Alonso became the first Chelsea player to be sent off in the Champions League since John Terry in April 2012 against Barcelona.
A trip to Bournemouth comes up next for Chelsea as the Blues aim to consolidate their place in the Premier League's top four. Bayern, meanwhile, are back in Bundesliga action against Hoffenheim on Saturday.