Chelsea were punished for a profligate showing at Borussia Dortmund after Karim Adeyemi's second-half strike secured a slender 1-0 lead in the Champions League last 16.
Graham Potter's side will have home advantage in the return match at Stamford Bridge on March 7 but left Signal Iduna Park ruing missed chances on Wednesday.
Joao Felix spurned a pair of glorious first-half opportunities in an entertaining encounter in Germany, before Adeyemi's 63rd-minute goal inflicted further misery on Chelsea after a ruthless counter-attack.
The Blues still have the chance to turn the tie on its head, but Potter and his men cannot afford similar struggles in front of goal in the second leg in west London.
Thiago Silva had the ball in the back of the net after 16 minutes, only to see the goal ruled out and the centre-back cautioned for a seemingly intentional handball past Gregor Kobel.
Chances continued to flow in a frenetic first half as Marius Wolf sliced a golden opportunity wide and Sebastien Haller fired narrowly off target from a presentable opening.
Joao Felix wastefully blazed over before hitting the crossbar after a driving run, while Wolf arrowed just wide with Kepa Arrizabalaga scrambling.
Kobel produced an expert stop to deny Reece James' pinpoint free-kick after the interval, before the Dortmund goalkeeper thwarted a bouncing volley from the England right-back soon after.
Adeyemi was clinical when Dortmund broke from the resulting corner, released by Raphael Guerreiro and powering past Enzo Fernandez before rounding Kepa to score.
Emre Can then cleared off the line after Kalidou Koulibaly's effort squirmed under Kobel, who kept Dortmund's narrow lead intact with a fine stop from Fernandez in the final minute.
What does it mean? Advantage Dortmund
Dortmund defeated an English side in European competition for the first time in 11 attempts, although their first such victory since March 2016 – against Tottenham – came with a degree of fortune.
Potter will wonder what his Chelsea side must do to get past Kobel in the return meeting after Joao Felix's pair of misses came back to haunt the Blues on the road.
A repeat performance at home may be enough to down Dortmund, but Potter's men cannot bank on having such a plethora of chances again as they stare down the barrel of an early European exit.
Adeyemi the difference
While the brilliant Brandt created four chances in a productive display, Adeyemi will steal the headlines for his remarkable goal on the break.
The 21-year-old has scored in each of his last three competitive appearances – one more than in his first 20 games for BVB.
Havertz's Dortmund wait goes on
Kai Havertz has repeatedly been trusted by Potter to lead Chelsea's line, but the Germany international suffered a familiar fate against BVB.
The forward managed to create four chances and also attempted four shots, but he has now played eight games against Dortmund without scoring – more than against any other opponent in his club career. He has lost all five away games against Dortmund.
What's next?
Chelsea return to Premier League action at home to Southampton on Saturday, while Dortmund host Hertha Berlin the following day in the Bundesliga.
Bayer Leverkusen 2-3 Leipzig: Visitors fightback halts unbeaten streak for Alonso's side
Bayer Leverkusen suffered their first defeat in 36 Bundesliga matches, as Leipzig came from behind to stun Xabi Alonso's side 3-2 at BayArena.
Lois Openda struck twice for Marco Rose's, who recovered from 2-0 down to make it two wins from two and move to the summit of the table.
It looked like business as usual for the reigning Bundesliga champions when they scored twice in the last seven minutes of the first half through Jeremie Frimpong and Alejandro Grimaldo.
However, Leipzig replied deep into first-half stoppage time with Kevin Kampl reducing the deficit.
Openda then brought the visitors level in the 57th minute, before a stunning long-range strike completed the turnaround 10 minutes from time, condemning Leverkusen to their first league defeat in 15 months.
Data Debrief: Leverkusen's long streak comes to a shuddering halt
Leipzig became the first side to beat Leverkusen in a Bundesliga match since Bochum achieved the feat a staggering 462 days earlier.
The visitors have begun a Bundesliga season with two wins from two for only the second time, also doing so in 2019-20.
They are also now unbeaten in 13 league matches, their longest such streak since Rose took charge.
As for Leverkusen, their invincible streak is officially history, as is their 29-game unbeaten run on home soil.
'We really let ourselves down' - Coleman slams Everton after late Bournemouth collapse
Seamus Coleman acknowledged Everton "really let ourselves down" and must "look at ourselves in the mirror" following their spectacular late collapse against Bournemouth.
Sean Dyche's side, who were seeking their first points of the season, led 2-0 in the 87th minute at Goodison Park through goals from Michael Keane and Dominic Calvert-Lewin.
However, the hosts were undone by three crosses in the latter stages, with Antoine Semenyo pulling a goal back and Lewis Cook levelling, before Luis Sinisterra completed a sensational turnaround in the sixth minute of stoppage time.
Boos rung around Goodison Park as the Toffees remained pointless and rooted to the foot of the Premier League table, and Coleman echoed the supporters' frustrations.
"We really let ourselves down in front of our fans," the skipper said. "We cannot take our foot off the gas at this level. Unfortunately, we did that.
"We cannot be conceding the goals that we did. We have to look at ourselves in the mirror."
Meanwhile, Dyche bemoaned the lack of responsibility amongst his players, as they became the first side in Premier League history to lose a game after leading by two or more goals in the 87th minute.
"We did so much right until they scored their first goal," the Everton head coach said. "The game should have been out of sight. We conceded one and then threw it away. I can't put my finger on it right now.
"They kept raining it forward and got their reward in the end. They were playing it forward and crossing it into the box, and we didn't deal with it. Simple stuff, but we threw it away. It is the third game we have thrown away this season.
"Everyone was looking at someone else to deal with things and that is when there is trouble. You could see the body language change. You have to see games through, and we have enough experience to do that, but today we didn't."
Bournemouth boss Andoni Iraola added: "It was the worst game we played this season. Everton deserved to win today, but the players kept pushing.
"I always have hope because this team has spirit. We have done it before and had some good comebacks. The spark of the first goal made us believe we could do it again."
Werder Bremen 0-0 Borussia Dortmund: Schlotterbeck sent off as BVB are held
Borussia Dortmund were held to a 0-0 draw at Werder Bremen in the Bundesliga on Saturday.
Defender Nico Schlotterbeck was sent off for Dortmund in the second half and Nuri Sahin’s side ultimately had to settle for a point.
After an underwhelming start to the match, the visitors were more aggressive following the interval, with substitute Karim Adeyemi making an instant impact with an effort from more than 20 yards out. But Bremen goalkeeper Michael Zetterer was in place to deny the forward.
Dortmund were reduced to 10 men in the 73rd minute when centre-back Schlotterbeck received a second yellow card for sliding in on Bremen forward Justin Njinmah.
BVB still pushed for a winner despite their numerical disadvantage, but a solid Bremen defence withstood late pressure to secure a point at home.
Data Debrief: Defences on top
Neither side can claim they were hugely unfortunate not to have scored, with Dortmund’s expected goals (xG) total of 0.61 only coming in marginally ahead of the hosts (0.41).
BVB did have four shots on target, although all four came from the 58th minute onwards with two of them from substitutes in Adeyemi and Donyell Malen, while Bremen only tested Gregor Kobel – who now has two straight clean sheets – on one occasion.
It was Marvin Ducksch who had the hosts’ only shot on target in his 100th Bundesliga appearance, the first six of which came as a Dortmund player.
The result means Bremen end a run of four straight home defeats to Dortmund in Bundesliga play, although they have now gone nine such matches without a victory.
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