The match was rescheduled from Tuesday night following explosions near Dortmund’s team bus, which saw defender Marc Bartra receive surgery on his wrist, though Dortmund manager Thomas Tuchel admitted before the game his team needed more time to prepare themselves.
Fabinho put a penalty wide after 17 minutes after Mbappe was brought down by Sokratis, but Mbappe himself put Monaco ahead two minutes later from close range, though he was in an offside position.
Sven Bender headed into his own goal before half-time to make it 2-0 to Monaco, but Dortmund pulled one back after the break through Ousmane Dembele’s close-range finish.
But Monaco regained their two-goal cushion with 11 minutes remaining as Mbappe capitalised on a defensive mix-up to finish superbly past Roman Burki.
Shinji Kagawa halved the deficit again just five minutes later, finishing after a superb turn inside the area, but Monaco held onto the lead to take into the second leg on April 19.
Dortmund players wore shirts in support of Bartra in their pre-match warm-up, while both teams and sets of fans came together in solidarity following Tuesday’s attacks.
Tuchel said before the game that he felt “helpless” to the decision to play the game less than 24 hours after the incident, and would have preferred more time to prepare.
His players did start the game slowly as Monaco dominated the first half, but Fabinho missed from the spot after referee Daniele Orsata gave the visitors a controversial penalty for Sokratis’ arm across Mbappe, who went down easily.
Two minutes later, Mbappe was half a yard offside as Thomas Lemar’s cross came off his thigh six yards out, rolling into the net to give Monaco a soft lead.
Dortmund should have equalised just after the half-hour mark, only for Kagawa to drag a shot wide from 10 yards, and they were made to pay four minutes later.
Andrea Raggi’s superb left wing cross put Dortmund under pressure, forcing Bender to head into the bottom corner on the stretch with Radamel Falcao waiting behind him to touch the ball home.
Dortmund responded superbly in the second half, and made it 2-1 through Dembele just before the hour mark, the Frenchman slotting home into the empty net after Kagawa had rounded the goalkeeper.
Falcao later rounded Roman Burki before blazing over from an angle, but Monaco did regain their cushion through Mbappe, who stole the ball off Sokratis following Lukasz Piszczek’s loose back-pass before finishing superbly.
Dortmund made it 3-2 with six minutes remaining through Kagawa, who finished well after a smart turn under pressure in the area, but Pierre-Emerick Aubameyang missed a fine chance to level late on, heading over from close range from Dembele’s fine cross.
