Brahim scored the only goal in Los Blancos' 1-0 win in Eastern Germany, with an eye-catching strike early in the second half being all that separated the sides.
Real had to weather an intense Leipzig storm though, as goalkeeper Andriy Lunin was forced into nine saves across the 90 minutes.
The 14-time winners are in a comfortable position heading into the second leg, which will take place early next month, as the club look to avenge last season's semi-final elimination.
There were some concerns in the latter stages though, as Brahim limped off after feeling discomfort in a leg muscle while in possession, which almost resulted in a Leipzig equaliser, until Lunin denied Benjamin Sesko.
However, speaking to the press after receiving the Man of the Match award, Brahim revealed that there is nothing to worry about for the Real Madrid faithful.
«I feel good, I think my injury is not serious,» Brahim said, when asked about the issue.
Brahim was the man who came in to replace Jude Bellingham after the England international picked up an injury against Girona at the weekend.
The match-winner had kind words for his teammate too, stating: «I celebrated like that for Jude, he wanted to play this game, so this goal [is for] for him.»
It was just a fifth start in 11 games for the Spaniard, who has struggled to usurp Bellingham, Rodrygo or Vinicius Junior for regular minutes in the starting XI.
The goal tonight does mean that the 24-year-old has scored the only goal in a last-16 first leg in successive seasons for two different clubs, after also doing so for AC Milan against
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