Monaco took a two-goal lead in under 20 minutes through Kylian Mbappe from a rebound after a Benjamin Mendy long-range strike followed by Radamel Falcao’s free header. Marco Reus replied for the visitors two minutes after half-time.
Despite Dortmund improving in the second half and enjoying more of the ball, substitute Valere Germain sealed Monaco’s place in the semi-finals just seconds after coming off the bench.
The task was already tough for Dortmund with Monaco already leading 3-2 on a difficult night at Signal Iduna Park last week through an Mbappe double and a Sven Bender own goal.
Marc Bartra, who was injured in the explosions near the Dortmund team bus last week, travelled but did not feature in the squad. The second leg kicked off five minutes late, with Dortmund saying the police held the team bus at the hotel for 20 minutes without reason.
In the third minute, in front of a packed out crowd at the Stade Louis II, Monaco took the lead through their highly-rated youngster Mbappe. The 18-year-old pounced on a rebound from a Mendy shot from outside the box which was sloppily palmed out by Roman Burki. Mbappe’s opener makes him the first player to score in each of his first four Champions League knockout games.
The beginning of the match was end-to-end, with both teams leaving gaps in their defence. Pierre-Emerick Aubameyang came close with a first-time shot and Falcao narrowly missed his header at the near post, while Nuri Sahin also cracked the woodwork from a free-kick just outside the box.
Monaco showed their attacking prowess again when they took a 5-2 aggregate lead through Falcao just 17 minutes in. A cross into the box from Thomas Lemar was met by the unmarked Colombia international who had the simple task of nodding the ball into the bottom left corner, leaving Dortmund, who improved as the half progressed, with a mountain to climb.
Dortmund came out of the traps immediately in the second half as early substitute Ousmane Dembele crossed in for Reus to smash his first-time effort into the net, meaning the Bundesliga club needed three goals for victory at that point.
The match still remained very open as Falcao missed a free header moments later before the ball almost fell for Aubameyang to turn in a flicked cross from a corner. And 65 minutes in Falcao had a chance to completely kill the tie off, but showed complacency as he lazily chipped the ball over the bar when a simple finish would have sufficed.
Both goalkeepers would go on to have busy evenings. Burki did well to tip an Mbappe shot wide of the post while Danijel Subasic prevented Reus from scoring from close-range.
And despite Dortmund’s increasing dominance in possession, Germain sealed Monaco’s place in the semi-finals 21 seconds after coming off the bench with a simple finish following a slick counter-attack started by the dangerous Lemar.
