All four of the home side's goals came in the first period, with James Rodriguez, Lucas Vasquez and Jese Rodriguez joining Cristiano Ronaldo on the scoresheet as Los Blancos moved to within four points of the leaders Barcelona.
Only Pepe, Casemiro and Ronaldo kept their places in the Real Madrid XI from the team that lost to Wolfsburg in the Champions League last week, with Keylor Navas and Luka Modric dropping out of the squad altogether.
Gareth Bale, Toni Kroos, Marcelo and Danilo all dropped to the bench, while Karim Benzema missed out with a knee problem and skipper Sergio Ramos served a one-game suspension. There were starts in the final third for Vasquez and Jese, while Kiko Casilla, Alvaro Arbeloa, Isco and James also came into Zinedine Zidane's starting team at the Bernabeu.
As for Eibar, centre-back Mauro dos Santos missed out through suspension, which meant a start for Ivan Ramis alongside Aleksandar Pantic. Borja Baston, meanwhile, who has struck 17 La Liga goals this season, was left on the bench, with Sergi Enrich selected at centre-forward.
Eibar put themselves under pressure in the fourth minute when Dani Garcia brought Jese to the ground with a rash challenge and James stepped up to send a free kick past Asier Riesgo into the bottom corner for 1-0. Ronaldo looked the favourite to strike it, but it was James that stepped forward to hand the hosts a fifth-minute advantage.
The away side's first strike towards goal came in the 12th minute when Keko found some space outside the Real Madrid box, but the attacker's effort was always too high.
Real Madrid had their second in the 18th minute, however, when Ronaldo used his strength to hold off Pantic before setting up Vasquez, who scooped the ball home from close range.
Less than 60 seconds later, it was three for the home side as Jese raced clear before finding Ronaldo, and the Portuguese registered his 30th league goal of the season.
Eibar's insistence on operating with a high defensive line continued to invite Real Madrid forward and only a couple of offside calls prevented the home side from isolating Riesgo in the Eibar net once again.
Ronaldo turned on the burners as Real Madrid counter-attacked once again 10 minutes before the break, but the Portuguese just could not slide a pass in to Jese, who would have had an easy tap-in for 4-0.
The Ronaldo-Jese combination did work in the 39th minute, however, when the Portuguese raced down the left before picking out a fine pass into the 23-year-old, who had the simple task of beating a hapless Riesgo from close range.
Eibar came close to a consolation late in the first period when Pantic rose highest inside the Real Madrid box, but Casilla, on his first league appearance since November, made a fine stop.
Both goalkeepers had to be at their best in the early stages of the second period, with Casilla keeping out a close-range Baston strike, before Riesgo palmed away a Ronaldo header down the other end moments later.
The end-to-end period continued at the Bernabeu as Enrich had a half-chance for the visitors and Ronaldo fizzed a long-range strike wide of the post in what was an open and expansive game of football.
Eibar continued to enjoy time and space in the final third and David Junca looked to pick out the bottom corner from a dangerous position in the 55th minute, but his strike just missed the post.
Junca, Enrich, Baston and Keko were almost operating as a front four for Eibar as the match entered its final 25 minutes, and Real Madrid did not look too comfortable at the back when they were put under pressure.
Ronaldo should have had his second of the match in the 74th minute when Vasquez put one on a plate for the Portuguese, but the league's top scorer somehow bundled his effort wide of the post.
Eibar then should have registered in the 80th minute when Baston met a deep cross at the far post, but somehow the striker rattled the crossbar with a close-range header on what was a frustrating afternoon for the visitors.
Real Madrid's focus will now switch to their Champions League quarter-final second leg against Wolfsburg on Tuesday, while Eibar, who remain 10th, will attempt to end their rotten run of league form when they host Real Sociedad next weekend.