But many of the powerhouse's fans are questioning the manager just three months into his tenure after Barcelona routed Madrid 4-0 at the Santiagao Bernabeu last weekend, leaving the humbled hosts in third place and six points adrift of the Catalan club at the top of the table.
Madrid's most disgruntled supporters waved white handkerchiefs to demand the removal of Benitez and shouted for club president Florentino Perez to step down.
Perez publicly declared that the club backed Benitez, but that was before Madrid almost blew a four-goal lead as it hung on 4-3 at Shakhtar Donetsk in the Champions League on Wednesday.
That unseemly performance for a team that boasts Cristiano Ronaldo and Gareth Bale at the head of a talented, and handsomely paid squad sets up the unforeseen scenario of Benitez under extreme pressure to get not just the three points but also a convincing victory at Eibar.
Madrid's troubles started before the "clasico" debacle. The team hasn't played up to its potential for the past four matches, which included an uninspired 1-0 win over Paris Saint-Germain and a 3-2 loss at Sevilla.
But Benitez insists on remaining optimistic and pointed to his team rediscovering its scoring punch at Shakhtar, instead of its porous defense that has conceded 10 goals in the last three matches.
"After the game against Barcelona, to respond like this and go ahead 4-0 appears to be positive to me," Benitez said. "I want to take away the positive aspects and we will analyze the mistakes we made."
Leader Barcelona, meanwhile, will look to continue its superb form against Real Sociedad on Saturday, when second-place Atletico Madrid hosts Espanyol trailing the pacesetters by four points.
Sevilla also welcomes Valencia on Sunday after both lost in the Champions League.
Here are some more things to know about the Spanish league's 13th round of matches:
FINDING A FIX
Benitez overhauled his lineup against Shakhtar from the starting 11 that imploded against Barcelona.
Forced because of injuries to replace Sergio Ramos and Marcelo with Pepe and Nacho Fernandez, he also made five other changes.
Midfielders Francisco "Isco" Alcarcon, Casemiro and Mateo Kovacic replaced striker Karim Benzema and midfielders James Rodriguez and Toni Kroos, while Dani Carvajal got the nod over Danilo at right back and Kiko Casilla was in goal instead of Keylor Navas.
The move to bulk up Madrid's midfield appeared to work until Shakhtar's late onslaught left Madrid on the verge of surrendering the win.
"We have to increase our competitiveness," Benitez said.
Madrid's already thin backline took another hit when Raphael Varane picked up an injury in Lviv.
Isco won't be available either for Eibar after he received a two-game suspension for kicking Neymar in the "clasico."
With Benzema still not fully fit after recovering from an injury and possibly distracted by his involvement in a blackmail investigation in France, Benitez may opt to again leave Ronaldo and Bale alone in attack.
SMALL BUT DEADLY
Eibar is one of the most modest clubs in the topflight, with a stadium that seats fewer than 7,000 and a 2013-14 budget of ‚¬18 million (now $19 million) compared to Madrid' â‚¬540 million (now $572 million).
But the Basque club is enjoying an excellent second season in the topflight and is in sixth place with only two losses through 12 rounds.
Striker Borja "Baston" Gonzalez leads the team with six goals. Attacking midfielder Sergio "Keko" Gontan, however, is suspended.
KEEP IT ROLLING
Barcelona looks unstoppable after crushing Madrid and routing Roma 6-1 in the Champions League on Tuesday, when Lionel Messi scored his first two goals since recovering from a knee injury.
Luis Enrique's team has outscored opponents 18-1 in its last five games, while Neymar and Luis Suarez lead the league with 12 and 11 goals, respectively.