Los Blancos were not tested on Saturday, though, frustrated only by offside calls and their own finishing either side of Marco Asensio's 41st-minute strike before Karim Benzema made sure 17 minutes from time.
Although Atleti and Barca – now third behind Zinedine Zidane's side – are both still to play this weekend, Madrid's title rivals will do well to find opponents as accommodating as Eibar.
An awful blind pass from Alejandro Pozo sent Benzema clear three minutes in, but the striker delayed before shooting and allowed Marko Dmitrovic to make a brilliant right-handed save.
Benzema was quickly denied again, this time by the offside flag after nodding in Marcelo's cross at the far post.
Asensio saw a wonderful free-kick bounce away off the crossbar and then joined Benzema in having a breakthrough goal struck off, his exquisite flick nutmegging Dmitrovic but drawing the attention of the VAR – again for offside.
Fortune soon found Asensio's favor, however, as he charged onto Casemiro's pass and slipped while shooting, only for his effort to clip his standing foot and beat Dmitrovic.
A second-half storm briefly threatened to derail Madrid, notably when Lucas Vazquez's backpass picked up pace on a slick pitch and required a desperate lunge from Thibaut Courtois to divert it to safety.
But after falling foul of the flag for a third time – Casemiro disappointed by team-mates standing in Dmitrovic's line of sight – Benzema wrapped up the result with a downwards header from substitute Vinicius Junior's fine centre.
What does it mean? First hurdle cleared with minimum of fuss
The weather was Madrid's most dangerous opponent against relegation-threatened Eibar. The same will not apply when Liverpool and Barca make the trip to Valdebebas.
Injured captain Sergio Ramos will be far more of a miss in those matches, but it was still important for Zidane – unbeaten against Eibar in 10 LaLiga meetings – to get three points on the board at the start of a monumental month.
Timely reminder of Marcelo's talents
This was just a ninth league outing of the season for Marcelo, who lined up on the wing with the security of fellow left-back Ferland Mendy behind him. It was a role that suited him well and no doubt gave Zidane pause for thought ahead of a big Champions League tie.
Given the license to attack without worrying about protecting a defence missing Ramos, Marcelo was a constant threat. Only the offside flag meant his final-third contributions – one blocked shot, one successful cross and no chances created – were relatively modest.
Benzema belatedly breaks through
Madrid's number nine was LaLiga's Player of the Month for March with five goals in three games, but he initially appeared to have left his fine form on the other side of the international break.
Benzema's third-minute chance really should have brought the opener, while mistimed headers followed either side of his disallowed effort. Finally, he found his range with the fourth of five attempts before being substituted with 10 minutes to go ahead of a season-defining stretch.
Madrid have three days to prepare for the visit of Liverpool, while Eibar do not play again until next Saturday, at home to Levante.