All three goals came in the second half, with France international Benzema breaking the deadlock on the hour mark, before Asensio came off the bench to instantly score in his first appearance after 330 days’ out with a knee injury.
Benzema settled the match in the 86th minute with a sublime volley after expertly bringing down Asensio’s pass.
“It was all very fast,” Benzema said. “It was a pass from Marco and I controlled the ball.
“It worked well, then I hit it with my left foot and it went in.
“It sounds easy when I explain it, but it’s about doing it in one quick movement.”
The result keeps second-placed Real Madrid in touch with leaders FC Barcelona who won 2-0 over bottom club Leganes on Tuesday. Real trail Barca by two points.
Real boss Zinedine Zidane was delighted with the win, but also the return of Asensio who injured his knee in pre-season against Arsenal in July.
“It means a lot, especially for him,” the Frenchman said.
“We are happy to see Marco on the pitch after eight months and then to score a golazo on his first touch, I’m very happy fro him.”
Barcelona have a tough assignment this weekend, travelling to third-placed Sevilla on Friday, while Real go to sixth-placed Real Sociedad on Sunday.