Vinicius and Marco Asensio both profited in the first half after darting behind Liverpool's makeshift back-line before a simple move from a throw-in gave Vinicius a simple finish in the second.
With Liverpool to come in the Champions League and a Clasico against Barcelona, Madrid welcomed a comfortable win thanks to goals from Marco Asensio and Karim Benzema.
Militao was shown a red card in the ninth minute at the Alfredo di Stefano Stadium, with his team already without their injured captain Sergio Ramos and COVID-stricken coach Zidane.
LaLiga: Lionel Messi, Antoine Griezmann net two each as Barcelona rout Granada; Sevilla edge Real Sociedad
Second-placed Real Madrid were one point behind Atletico after being held at Osasuna to 0-0 in a match played in steady snowfall and with barely any scoring chances for either side.
Bilbao proved to be tough opponent at Alfredo Di Stéfano stadium despite playing most of the match with only 10 men. But when the Basque Country team was threatening to at least salvage a point, Benzema scored his team-high ninth and 10th goals of the season.
UEFA Nations League: Real Madrid's Marco Asensio to replace injured Barcelona forward Ansu Fati in Spain squad
Fati injured his left knee in Barcelona's 5-2 win over Real Betis in the Spanish league on Saturday.
Zidane had to experiment in Real Madrid's defence with Sergio Ramos and Dani Carvajal serving suspensions and Marcelo and Nacho Fernández injured.
LaLiga: Karim Benzema's brace propels Real Madrid to comfortable victory over Valencia; Real Sociedad lose to Alaves
Karim Benzema scored twice and Marco Asensio added another on his return from a 10-month injury layoff as Real Madrid beat Valencia 3-0 on Thursday to keep pace with leader Barcelona in the Spanish league.
LaLiga: Eden Hazard, Marco Asensio back for Real Madrid return against Eibar, says manager Zinedine Zidane
Real Madrid’s joint-record signing Eden Hazard and Spain international Marco Asensio are both fit for the team’s first LaLiga match in over three months against visitors Eibar on Sunday, coach Zinedine Zidane has said.
LaLiga: Real Madrid forward Gareth Bale set to miss upcoming league Espanyol game, Champions League fixture against Club Brugge
Other Madrid players who did not practice with the rest of the squad on Friday included Eden Hazard, James Rodríguez, Marcelo, Marco Asensio and Lucas Vázquez
LaLiga: Real Madrid's injury woes worsen as Isco faces upto three weeks on sidelines after picking up thigh injury
The injury to Isco is another setback for Zinedine Zidane's team which already has a lengthy injury list featuring Eden Hazard, James Rodriguez, Brahim Díaz, Rodrygo and Marco Asensio
LaLiga: Real Madrid's available squad shrinks yet again as newly-acquired youngster Brahim Diaz suffers thigh injury
Madrid says tests conducted Tuesday show midfielder Brahim Díaz has a muscle injury in his thigh. The club has not said how long he is expected to be sidelined
LaLiga: Real Madrid boss Zinedine Zidane says he will count on winger Gareth Bale for upcoming season
Real Madrid manager Zinedine Zidane said that he'll be counting on Gareth Bale to deliver in the absence of Eden Hazard and will look to utilise him adequately
LaLiga: Real Madrid midfielder Eden Hazard to miss season-opening clash against Celta Vigo due to thigh injury
Eden Hazard has picked up a muscular injury to his right thigh during practice and is likely to be out for three to four weeks for Real Madrid
Real Madrid's Ferland Mendy has been added to Zinedine Zidane's growing injury list after the Spanish club confirmed on Thursday the France left-back had suffered a calf injury.
LaLiga: Real Madrid winger Marco Asensio could miss most of season after rupturing ACL during friendly against Arsenal
Real Madrid winger Marco Asensio ruptured his anterior cruciate ligament during a friendly against Arsenal, the Spanish club announced Wednesday, and is expected to miss most if not all of the next LaLiga season.
International Champions Cup: Out-of-favour Gareth Bale scores on return as Real Madrid edge past Arsenal on penalties
Real Madrid clawed back from two goals down to finish full time at 2-2, and prevailed 3-2 in the penalty shootout dictated by the International Champions Cup exhibition tournament format.
Euro 2020 qualifiers: Alvaro Morata nets brace to continue remarkable revival as Spain see off Malta
Alvaro Morata's remarkable revival continued on Tuesday as he scored twice for Spain in a 2-0 victory over Malta.
Champions League: Real Madrid's Sergio Ramos charged by UEFA for drawing deliberate booking during tie against Ajax
Real Madrid centre-back Sergio Ramos was charged by UEFA on Tuesday for "receiving a yellow card on purpose" during their Champions League last-16 tie with Ajax.
La Liga: Lionel Messi's fitness, Philippe Coutinho's form trouble Barcelona; Real Madrid bank on Vinicius Junior
Barcelona will hope to reassert their authority in the title race on Saturday after a stuttering spell has given Real Madrid fresh hope in La Liga.