Valencia defender Gabriel Paulista was shown a straight red 18 minutes from time for chopping down Vinicius with a wild tackle that almost started a brawl among players on the pitch.
The La Liga champions climbed to 45 points in second place in the standings, five behind leaders Barcelona.
Valencia, who fired manager Gennaro Gattuso on Wednesday, are on a five-game winless streak and are 14th on 20 points, one clear of the relegation zone.
Real, bidding to retain the title, are under pressure from their arch-rivals Barca who are unbeaten in their last 14 matches in all competitions and on a four-game winning streak in LaLiga.
They were the better side for large parts of the game and controlled the tempo on a chilly night in Madrid, but it took them a while to find their mojo in front of goal, with Vinicius and Karim Benzema wasting good opportunities in the first half. Antonio Rudiger had a goal ruled out by VAR for a Benzema foul in the build-up just before halftime.
Real looked sharper after the break, however, and struck twice in two minutes, a magnificent curling shot into the top corner by Asensio after 52 minutes followed by Vinicius slotting home from close range to finish off a lightning quick counter-attack. Real controlled the rest of the game against opponents whose frustration was shown by Paulista's reckless challenge on Vinicius.
"We need to protect Vinicius," Real Madrid goalkeeper Thibaut Courtois told DAZN. "He is a very fast and explosive player that uses a lot of dribbling. Defenders don't like it. They feel they're being provoked, but it's his way of playing.
"I'm happy that today a referee had the courage to show the red card because it's a tackle without the ball, meaningless. Not only to Vini, to anyone." It was not all good news for Real Madrid, however, with defender Eder Militao and forward Benzema, key players for coach Carlo Ancelotti, leaving the match early due to leg injuries.
Real Madrid play Mallorca in LaLiga on Sunday and travel to Morocco on Monday for the FIFA Club World Cup. "This is what happens when you play every three days," Ancelotti said. "Militao is out for Sunday but Benzema (injury) looks to be minor."
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