The home win on Thursday left Madrid two points behind Barcelona, which defeated Legans 2-0 on Tuesday for its second straight win after the pandemic break.
Madrid took control of the match after a lackluster first half in which Valencia had the most significant scoring chances and a goal disallowed by video review.
Benzema opened the scoring in the 61st minute after a pass by Eden Hazard, who again was decisive for Madrid in his second match after a long injury layoff.
Asensio, making his first appearance since a serious knee injury last year, scored with his first touch about 30 seconds after entering the match in the 74th.
That's the way to come back, his teammates could be heard saying during the goal celebration at the empty Alfredo Di Stfano Stadium.
I couldn't wait to come back after so many months of hard work, said Asensio, who was injured in a friendly last July. I'm glad that I'm back and that I was able to score."
Asensio also set up Benzema's third goal with a one-touch cross on a counterattack and the French striker finished off the move sublimely using his right foot to flick the ball away from a defender and then his left to hammer it into the top of the net. It was the Frenchman's 16th league goal to leave him five behind scoring leader Lionel Messi.
Zinedine Zidane reaches new milestone after victory over Valencia
After a commanding victory over Valencia, Real Madrid manager Zinedine Zidane reached a new milestone as he now has the second-highest number of wins by any coach in Real Madrid history.
With this victory, the Frenchman has won 133 games, equalling Vicente Del Bosque. Zidane now only sits behind only Miguel Munoz, who picked up 357 Whites' wins.
All these victories have led to Zidane clinching 10 titles as Real Madrid coach which includes three Champions Leagues, two Club World Cups, two European Super Cups, one La Liga, and two Spanish Super Cups.
Moreover, he has taken charge of 201 Real Madrid games, sitting third in the all-time list for most games managed, behind Del Bosque (246) and Miguel Munoz (605).
It was the fifth double this season for Benzema, who passed Ferenc Puskas to become Madrid's fifth leading scorer all-time.
Valencia went a man down in the 89th after a straight red card was shown to South Korean midfielder Lee Kang-in for a foul on Madrid defender Sergio Ramos. A few moments later, midfielder Francis Coquelin had to leave injured after the team had already made all five substitutions.
Valencia is winless after the break and dropped to eighth place. It had the best chances early on, with Rodrigo hitting the far post after a breakaway in the 14th. His goal a few moments later was disallowed by video review after a close offside call.
It was Madrid's second straight game at its training centre, which is being used while the Santiago Bernabu Stadium remains under renovation until the end of the season.
La Liga points table as of June 19, 2020:
| La Liga points table | ||||||||
| Club | Matches played | Won | Draw | Lost | Goal for | Goal against | Goal difference | Points |
| Barcelona | 29 | 20 | 4 | 5 | 69 | 31 | 38 | 64 |
| Real Madrid | 29 | 18 | 8 | 3 | 55 | 20 | 35 | 62 |
| Sevilla | 29 | 14 | 9 | 6 | 42 | 30 | 12 | 51 |
| Atletico Madrid | 29 | 12 | 13 | 4 | 37 | 22 | 15 | 49 |
| Getafe | 29 | 13 | 8 | 8 | 38 | 27 | 11 | 47 |
| Real Sociedad | 29 | 14 | 5 | 10 | 46 | 36 | 10 | 47 |
| Villarreal | 29 | 13 | 5 | 11 | 46 | 38 | 8 | 44 |
| Valencia | 29 | 11 | 10 | 8 | 39 | 43 | -4 | 43 |
| Granada | 29 | 12 | 6 | 11 | 37 | 35 | 2 | 42 |
| Athletic Club | 29 | 9 | 12 | 8 | 32 | 29 | 6 | 39 |
| Levante | 29 | 10 | 5 | 14 | 34 | 42 | -8 | 35 |
| Alaves | 29 | 9 | 8 | 12 | 31 | 39 | -8 | 35 |
| Osasuna | 29 | 8 | 11 | 10 | 35 | 44 | -9 | 35 |
| Real Betis | 29 | 8 | 10 | 11 | 40 | 47 | -7 | 34 |
| Valladolid | 29 | 7 | 12 | 10 | 25 | 34 | -9 | 33 |
| Eibar | 29 | 7 | 7 | 15 | 30 | 46 | -16 | 28 |
| Celta Vigo | 29 | 5 | 12 | 12 | 22 | 35 | -13 | 27 |
| Mallorca | 29 | 7 | 4 | 18 | 28 | 49 | -21 | 25 |
| Espanyol | 29 | 5 | 9 | 15 | 25 | 46 | -21 | 24 |
| Leganes | 29 | 5 | 8 | 16 | 22 | 43 | -21 | 23 |
Other La Liga match results
Real Sociedad stalls
Real Sociedad failed to regain fourth place after a 2-0 loss at Alavs in which it couldn't get a single shot on target.
Borja Sainz opened the scoring with a goal awarded following video review in the 56th, and Martn Aguirregabiria sealed the victory deep in stoppage time at the Mendizorroza Stadium.
A victory would have sent Sociedad past fourth-place Atltico Madrid, which won 5-0 at Osasuna on Wednesday. It stayed in sixth instead, two points from the final Champions League spot.
Sociedad went a man down in the 81st as defender Joseba Zalda was sent off with a second yellow card, but Alavs was also reduced to 10 men six minutes later when midfielder Toms Pina was shown a second yellow.
Sociedad had won four of its last five league games before the break, with its only setback a loss at Barcelona. Its first match after the league resumed was a 1-1 draw against midtable Osasuna at home.
We didn't play our best today, and we hadn't played our best in the previous match either, Sociedad midfielder Igor Zubeldia said.
We need to improve for our next match. Sociedad will next host Real Madrid, while Alavs visits Celta Vigo.
Alavs, which hadn't won in three straight league matches, moved to 11th place.
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