Galacticos Kylian Mbappe, Vinicius Junior and Jude Bellingham all scored in a thrilling 3-2 win at Italian league leader Atalanta on Tuesday night.
But Madrid still had to ride their luck as Mateo Retegui fired over from in front of goal in stoppage time when handed a golden chance to level the game.
It was only Madrid's third win in the competition's revamped league phase and leaves the 15-time champions in the unseeded playoff positions in 18th place.
Liverpool lead the way after maintaining their perfect record in Europe this season with a 1-0 win against Girona.
Like Madrid, Paris Saint-Germain also picked up a much-needed win, beating Salzburg 3-0 to sit in the last playoff spot in 24th place.
Bayer Leverkusen are second after a 1-0 win over Inter Milan, while Aston Villa beat Leipzig 3-2 and are third.
Brest beat PSV Eindhoven 1-0 and are fifth. Eighth-place Bayern Munich routed Shakhtar 5-1.
Mohamed Salah's 50th Champions League goal maintained Liverpool's perfect record in the competition this season.
The Egypt forward struck a 63rd minute penalty to seal the win in Spain that kept Liverpool atop the 36-team league.
Liverpool's Mohamed Salah scores the opening goal against Girona from the penalty spot. (AP PHOTO)
But even after a sixth straight win for the Merseyside club, head coach Arne Slot was critical of his players in a game that saw goalkeeper Alisson pull off several saves to keep Girona out.
"If you ask me about all the six games, I'm really pleased with all the results, I am really pleased with the five (other) games with the way we played. I'm far from pleased about the performance tonight," he said.
Salah's goal was his 16th in 22 appearances overall this season.
Girona were 30th with just one win from six games.
"I almost feel sorry for them because they deserved so much more in this Champions League campaign than the three points they have until now. But we have an incredible goalkeeper," Slot said.
Six-time European Cup winner Liverpool are looking like the team to beat in the Champions League this season after big wins against holder Real Madrid and German champion Bayer Leverkusen last month.
They continued their outstanding start to the campaign, which also has them on top in Premier League.
Former Manchester United midfielder Donny van de Beek handed Salah the chance to fire the visitors ahead with a clumsy tackle from behind on Luis Diaz in the box. Salah stepped up to convert the penalty and Girona goalkeeper Paulo Gazzaniga went the wrong way.
Liverpool's two remaining games are against Lille at home and PSV Eindhoven away in January.
US international Christian Pulisic is the only player to have scored against Liverpool in this season's Champions League in a 3-1 loss for Milan in September.
Dinamo Zagreb drew 0-0 with Celtic and both teams remain in the playoff positions.
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