But substitute Valere Germain, just after replacing Mbappe, added the third in the 81st minute to seal a 6-3 victory on aggregate. It was Monaco’s 141st goal of an incredible season that has captured the imagination and made the rest of Europe take notice.

“We knew they would give us space and we took advantage with the speed of our forwards. I think that today it could have ended up 5-3 or 6-3, because both sides missed chances,” Monaco coach Leonardo Jardim said. “We were very solid, but we also showed a lot of ambition. We never tried to protect the result, because our DNA is to attack and to always try and score.”

Dortmund coach Thomas Tuchel accepted that his side fell short.

“We knew we needed a performance of the highest level to turn things around, but that wasn’t the case,” he said. “We made too many basic errors in terms of our positioning and we didn‘t close them down enough in defense.”

Tuchel said that Monaco’s early goals “destroyed our belief a bit” and resulted in “too many mistakes” being made.

The home leg in Germany was overshadowed by an attack on the Dortmund team bus as it headed to the stadium. Prior to Wednesday’s game, Dortmund’s bus was held for nearly 20 minutes by police at the team hotel. Kickoff was briefly delayed.

Dortmund made the worst possible start to the match, conceding a goal after just three minutes.

Left back Bernard Mendy ran at the heart of Dortmund’s defense and hit a fierce shot that goalkeeper Roman Burki spilled. Mbappe slotted the loose ball into the bottom left corner for his 22nd goal of a breakthrough season that has made the 18-year-old one of the brightest prospects in European soccer.

He had scored twice in the first leg and in both legs against Manchester City in the Round of 16.

Falcao’s diving header, the 27th goal of his comeback season, made it 2-0 in the 17th minute.

Reus pulled one back when he turned in a right-wing cross from substitute Ousmane Dembele to offer some hope, before Germain sprinted through to send Stade Louis II crowd into raptures.

In the night’s other match, Barcelona went out after drawing 0-0 at home to Juventus, which won the first leg 3-0.

Monaco, which reached the semifinals in 2004 on its way to the final, will join 2015 runner-up Juventus, defending champion Real Madrid and beaten finalist Atletico Madrid in Friday’s tough draw.

“They are three big teams and have a lot of experience at this level,” Jardim said. “We have to make the most of this opportunity and to play with our qualities.”

After the drama of last week’s attack, this was a welcome return to euphoric, attacking football that was a joy to watch from start to finish.

Both sets of fans united in a touching show of support beforehand, singing the famed football anthem “You’ll Never Walk Alone” as they raised scarves together.

It was a frantic spell after Mbappe’s opener, with Monaco’s attacking midfielder Bernardo Silva and Dortmund’s Nuri Sahin going close.

Falcao then launched himself to plant a diving header past Burki -- a pure finisher’s goal to underline his return to the highest level after two frustrating seasons fighting his way back from a serious knee injury.

After Reus caught Monaco’s defense napping, Dortmund kept pushing forward in numbers. Monaco was stretched down both flanks but, equally, Dortmund was increasingly exposed to Monaco’s slick counterattacking.

Falcao lofted a shot narrowly over after breaking down the right in the 65th and Mbappe had a low shot saved moments later from a similar position.

Dembele and Reus continued to threaten, with Reus having a snapshot saved in the 73rd, while Monaco midfielder Tiemoue Bakayoko headed over and Mbappe failed to control a pass near the penalty spot as the chances came thick and fast on a chilly night.

Germain put the result beyond doubt as he broke through -- again down the right -- and slotted the ball under Burki’s body.

The whole Monaco bench rushed to jump on him: a symbolic image of Monaco’s teamwork.

“All the players played at a high level. Our defense was well organized and the midfield held their positions really well,” Jardim said. “It wasn’t a day for speaking about individuals. (AP)