Their victory at the Santiago Bernabeu may only give Madrid 24 hours above Barcelona, who play Girona on Sunday, with their perfect record still intact.
More pressing for Julen Lopetegui will be the defensive slackness that made this arguably the least assured of the six competitive games he has overseen so far, including last weekend's draw away to Athletic Bilbao.
There were changes, with Gareth Bale, Marcelo and Dani Carvajal all rested, the latter not even included on the bench, following Real's win over Roma in the Champions League on Wednesday.
But if they gift Atletico Madrid the same chances in the city derby next weekend, they may not find their opponents so generous. Atletico had earlier ground out a 2-0 win away to Getafe.
Benzema shines as Madrid rout Leganes
"The game was nervous and in the last 15 minutes we lacked control," Lopetegui said. "These post-Champions League games are always really dangerous and we know it."
Carvajal's absence meant a debut for Alvaro Odriozola, who joined from Real Sociedad in the summer, while Thibaut Courtois replaced Keylor Navas to continue Lopetegui's rotation strategy in goal.
The hosts were more impressive going forward and in the 41st minute, they took the lead. Luka Modric's scuffed shot landed kindly at the feet of Asensio and he did brilliantly to harpoon the ball into the far corner.
Referee Mateu Lahoz ruled the goal out for offside but Real were saved by VAR and then later the crossbar, as Borja Iglesias' scooped finish was denied late on.
"We are not going to win 5-0 every game," Varane said.
Atletico's victory was more comfortable and they had Thomas Lemar to thank after the Frenchman scored his first goal for the club and instigated another against Getafe.
The result was all but secure when Getafe's Ivan Alejo was sent off shortly after the hour for a dangerous tackle on Saul Niguez.
Atleti had not lost to Getafe, or even conceded a single goal, in 13 previous meetings but victory meant more to Diego Simeone's side after just one win from their opening four league games.
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