Marco Asensio had the first real chance of the match in the sixth minute after breaking into the Leganes box, but the Spaniard could only lift the ball over the crossbar.
The home side did take the lead in the 17th minute, however, when Bale's effort from a Dani Carvajal effort found a route into the back of the net despite the best efforts of Ivan Cuellar, who initially looked to have kept it out.
Leganes - under the management of former Southampton boss Mauricio Pellegrino - were level in the 24th minute though, with on-loan Saints forward Guido Carrillo converting from the penalty spot after Casemiro had brought Javier Eraso to the ground with a rash challenge.
The equaliser gave Leganes confidence, and Michael Santos brought a smart save from Thibaut Courtois in the period that followed, before Cuellar kept out a Bale header down the other end of the field.
Toni Kroos headed a Bale cross wide of the Leganes post late in the half as Real Madrid continued to boss the possession, while Benzema also tested Cuellar before the half-time whistle went at 1-1.
Benzema sent Madrid back ahead in the early stages of the second half, however, when he headed an Asensio cross into the bottom corner of the net.
The Frenchman's effort was initially chalked off for a foul on Leganes left-back Jonathan Silva, but following a VAR check, Los Blancos were ahead.
Benzema then scored his second of the match in the 62nd minute, with the Frenchman finding the bottom corner with a wonderful finish at the conclusion of what was a fine passing move.
Real Madrid's fourth arrived in the 66th minute when captain Sergio Ramos converted from the penalty spot after Unai Bustinza had brought Asensio to the deck with a rash challenge.
Isco almost had a low cross turned into the back of the Leganes net by Bustinza in the 73rd minute as Los Blancos continued to search for more goals on home soil.
Bale then fired over the crossbar following excellent work from Asensio, and the scoreline was certainly not flattering Julen Lopetegui's side due to their dominance on the night.
Isco should have made it five late on, but the Spaniard fired into the arms of Cuellar from close range as it finished 4-1 to the European champions at the Bernabeu.
REAL MADRID (4-3-3): Courtois; Carvajal, Ramos, Varane, Marcelo; Casemiro, Kroos, Modric (Isco 62'); Bale (Lucas 85'), Benzema, Asensio (Ceballos 78')
LEGANES (4-3-3): Cuellar; Juanfran, Bustinza, Siovas, Silva; Gumbau, R.Perez, Eraso (Vesga 70'); El Zhar (En Nesyri 70'), Carrillo, Santos (Rolan 81')