Cristiano Ronaldo moved three clear of Lionel Messi at the top of the Champions League scoring charts after a hat-trick against Shakhtar Donetsk.
His treble, which included two spot-kicks, took him to 80 Champions League goals and eight in his last two games.
Ronaldo's third was a header after Marcelo's shot had been parried.
Karim Benzema had tapped in Real's opener after keeper Andriy Pyatov dropped a cross, while Shakhtar had Taras Stepanenko sent off.
Real Madrid's main cause for concern from the game was forward Gareth Bale having to go off injured after 32 minutes.
The Wales international was holding his calf before being replaced by Mateo Kovacic, while the Spanish club's centre-backs Raphael Varane and Sergio Ramos were also substituted with knocks.
Ronaldo was level with Barcelona rival Messi on 77 Champions League goals before Real Madrid began their quest for a record 11th crown in Europe's top competition.
But after the Portuguese had bagged five goals against Espanyol on Saturday, he scored his third Champions League hat-trick to move clear on his own at the top.
Ronaldo and Messi have constantly overtaken each other for the honour of the competition's most prolific scorer and the latter will have the chance to respond when Barcelona meet Roma on Wednesday.
The first of Ronaldo's spot-kicks came after Darijo Srna was controversially adjudged to have handled the ball, despite a shot from the Real forward appearing to hit him on the back.
"I feel so proud and happy to score eight goals in two games but that is not my goal - my aim is to be good all season and for the team to succeed, which is the most important for me, and win trophies," said Ronaldo.
"It is just the beginning of the season. The league is long. It is too early to say we are amazing or bad. Let's work the same way and let's see what happens at the end of the season."
"Without playing a brilliant match we still created a lot of chances," said Real Madrid manager Rafa Benitez.
"Bale had a spasm in his calf muscle. We must wait a day or two to see how serious it is. He had a similar issue last year."
(BBC)
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