A big chance to go in front fell to Real when Marco Asensio broke into the opposition box, but he lifted the ball over the top of the goal on six minutes.
Real made the breakthrough as early as 17 minutes thanks to Gareth Bale who capitalised on a header from Dani Carvajal to grab his third of the campaign.
Before that, Los Blancos piled tantamount of crosses to the box, aiming to catch Leganes defence napping but the visitors stood tall and defended well.
The league’s new boys were level on 24 minutes when Guido Carrillo steered home from 12-yards despite the best efforts of debutant goalkeeper Thibaut Courtois.
Courtois made his first save for his new club denying Santos from point-blank range on 28 minutes after being caught napping.
A shot from Bale on 42 minutes outside the box, flew narrowly wide of target amidst a body of Leganes defenders.
The home side didn’t stop there searching for their second, as Karim Benzema forced a good save from Carlos Cuellar who made a firm save.
The Frenchman made no mistake shortly after the break, sending in a header to the far post after a cross from Marco Asensio, with VAR consultation awarding the strike in the end.
Benzema made Leganes pay for poor defending with his brace from outside the box, following an excellent team move allowing the Frenchman to find the bottom corner on 63 minutes.
Four minutes later, Real made it four from the penalty spot after a foul on Asensio inside the box. Sergio Ramos sent the spot kick into the back of the net.
The European champions controlled the game completely from then on, with Leganes flat out of their wrists.
Julen Lopetegui made a few changes, whilst instructing his charges to continue strutting their stuff with their off the ball movements.
As such, their campaign continues with the bright start, remaining top of the table with three wins in succession.