The visitors improved after half-time before Asensio finished off a ruthless 57th minute counter-attack to confirm a 10th consecutive win for Real in all competitions.
The result leaves Real Madrid in a dominant position at the top of LaLiga, eight points clear with 17 games played, after victories over fellow title contenders Sevilla, Real Sociedad and now Atletico in recent weeks.
"To win a derby is very important to our fans and I bet they left the stadium really happy," Asensio told reporters.
"Vinicius is playing really well, we are delighted with his progression this season. He is doing it all, scoring, assisting. We are all happy for him."
Atletico started brightly, and Thibaut Courtois had early work to do when he smothered Marcos Llorente's cross with Matheus Cunha -- picked ahead of Luis Suarez in Atletico's attack -- waiting to pounce.
After that, Real Madrid began to take control. Eder Militao's near-post header flew across the face of goal before Benzema, who has been LaLiga's outstanding player so far this season, opened the scoring.
Atletico's best opportunity came from Antoine Griezmann, whose free kick was saved by Courtois diving at full stretch, while at the other end Vinicius tested Oblak before half-time.
Both managers made changes at the break. Carlo Ancelotti withdrew goalscorer Benzema, replacing him with Luka Jovic, while Diego Simeone made a double substitution, introducing Joao Felix and Thomas Lemar for Griezmann and Yannick Carrasco.
"We were effective," said Ancelotti after the match, while adding his team were now clear LaLiga favourites. "We had solidity at the back. They played a lot of long balls, they tried to get in behind with Correa, we were a bit surprised that they played 4-4-2 so we had to push a bit more with our fullbacks, but after the first goal we controlled the game.
"We're favourites today, you can say that, of course. We've done well, better than the others. We're focused on the next games, dropping off mentally can cost you. We're doing well, we have to keep going, that is the only way to get closer to winning sooner."
The first chance of the second half fell to Asensio, who chose to turn into a crowd of Atletico defenders inside the box rather than getting a quick shot away.
Felix made an impact, forcing Courtois to save before playing in Cunha to do the same, before Atletico were undone on the counter.
Vinicius grabbed his second assist of the match, his final ball playing in Asensio to sweep clinically past Oblak.
Ancelotti had praise for Modric and others after the game: "Modric, the three points, the solidity at the back, the clean sheet, Courtois, Vinicius... there was a lot.
"[Modric] played a spectacular game in every sense, with the ball, without the ball, with personality and character, he's an extraordinary player."
Real's 2-0 victory means Atletico have now gone 11 LaLiga derbies without a win, a run stretching back to 2016. After the game, Atleti boss Diego Simeone admitted his side were up against a team at its best.
Simeone said: "In football being clinical is the most important thing. Madrid are absolutely clinical at the moment. They get a chance, and they score. From there, the game starts to change. We had some chances at the start of the second half, and then they used the counter-attack well and scored a great goal, and won the game fairly."