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.