The result snapped a three-game winless streak across all competitions for Los Blancos.

Olympiacos struck first in Piraeus when Chiquinho capped a slick passing sequence by driving a 20-yard effort into the net, but from that moment on, the night belonged to Mbappe, who surged to the top of this season's Champions League scoring chart with an incredible four-goal haul.

Madrid's equaliser arrived in the 22nd minute as the French star latched onto a superb Vinicius Junior through ball and slipped a low shot between the legs of goalkeeper Kostas Tzolakis. Just two minutes later, Mbappe headed Arda Guler's delivery into the net to put the Spanish giants ahead.

He completed his hat-trick by breaking clear of the defence and finishing calmly past Tzolakis again, with his treble clocking in at six minutes and 42 seconds - the second fastest in Champions League history, behind Mohamed Salah's hat-trick for Liverpool against Rangers in 2022.

Olympiacos forced their way back into the contest early in the second half when Mehdi Taremi powered a header beyond stand-in keeper Andriy Lunin.

But Vinicius' sharp work down the left created the opening for Mbappe to tap home his fourth goal, sealing the victory and lifting his tally to nine goals in five Champions League matches.

"It was very important to get back to winning ways, we know that three matches without that is a lot for us," Mbappe said in his post-match interview.

"I'm very happy, it's always a pleasure to score goals. My team-mates are giving me quality passes. I'm very lucky to play in this team, with these team-mates.

"Of course there are things to improve. At a club like Real Madrid (it's normal) that people talk."

Madrid coach Xabi Alonso reflected on the significance of the result afterward and what it meant to his squad.

"The important thing today was to break up, a little bit, the dynamic we were coming from, and to get back that (winning) feeling," he said.

"We need everyone, and it's clear that today Kylian stands out with the goals, but today it was very important to change the dynamic... and that's why the players were celebrating."

Elsewhere in Spain, Atletico Madrid also enjoyed a dramatic European night, pulling off a stoppage-time victory to keep their own Champions League hopes alive.

Jose Maria Gimenez struck a 93rd-minute header to hand Atletico a 2-1 win over Inter Milan, ending the Italians' perfect record in the competition.

Julian Alvarez had given the hosts the lead before Piotr Zielinski equalised, but Gimenez's late intervention left Inter stuck in a congested pack at the top of the table, while Atletico's win pushed them up to nine points.

Tapelo Xoki penalty gives Orlando Pirates victory over SuperSport United