Mbappe had the chance to open the scoring inside the first half-hour after Noussair Mazraoui clipped him in the box, but after a VAR check lasting more than three minutes, goalkeeper Yassine Bounou saved his tame effort down the middle. Morocco held firm for the rest of the first half, with France building up a huge share of possession and chances without finding a way through.
The breakthrough finally came in the 60th minute when Mbappe curled a brilliant effort past Bounou from the edge of the box, and six minutes later he turned provider, drawing defenders away to tee up Dembele for a low finish that made it 2-0. Mbappe was withdrawn in the 77th minute with what appeared to be an ankle knock but was well enough to join the celebrations afterwards.
Morocco coach Mohamed Ouahbi praised his side's effort despite the defeat.
"We have to admit we faced a very good opponent. We struggled a lot in the first half, and Bounou's penalty save kept us in the game. We defended better in the second half and were calmer in possession. In the end, it was an individual piece of brilliance from Mbappe.
"It was a difficult feeling, but we have to keep working. We need more options on the bench when we have injuries, absences and fatigue, but of course we're disappointed.
"The future will be bright if we continue like this, but that doesn't mean we didn't want to win today. Of course we wanted to win today. We did everything we could to win, but we faced a very difficult opponent. It's a disappointment, of course, but we'll keep working for the future. We know we represent more than just one country. We represent the Moroccan people, and many countries across Asia and Africa. Many people see themselves in this team, and we'll keep working to win titles in the future."
France head coach Didier Deschamps offered reassurance afterwards over the fitness of Mbappe and Manu Kone, who were both withdrawn during the game.
"No, Kylian - it's a bit of an ankle issue, he felt some pain, and Manu Kone took a knock on the knee and had a bit of cramp. Warren [Zaire-Emery] came on and did very, very well. They all need to be ready. I can't keep everyone happy, but I make sure they all feel involved," Deschamps told beIN Sports.
Mbappe explained afterwards what had gone wrong with his penalty.
"I hit my penalty badly, but it was a complicated situation, there was some confusion. The referee told me there was a penalty, so I got ready. Then he came to tell me maybe there wasn't a penalty. I let myself get distracted, I didn't know that scenario yet," he said. His overall penalty record for France remains outstanding: 14 goals from 16 attempts.
Dembele, who has now scored five goals at this World Cup, explained his role in the second goal.
"Kylian told me just before to stay central. That we were going to get the chance on the counter-attack, and that's what happened. He made a brilliant run to leave me space. I saw it was a bit open and I tried to keep my shot on target, and it worked out," he told M6.
France will face the winner of Spain's quarter-final with Belgium in the semi-final in Dallas.