Gareth Bale's header and Cristiano Ronaldo's penalty eased the pressure on manager Rafael Benitez as Real Madrid earned an unspectacular win at Eibar.
Bale glanced in a Luca Modric cross just before half-time to claim his third goal of the season.
Ronaldo then scored his 16th after Lucas Vazquez was tripped late on.
Real avoided a third successive league defeat for the first time since the end of the 2008-09 season to move six points behind leaders Barcelona.
•Relive how Real won at Eibar
Benitez had received the backing of Real Madrid president Florentino Perez following his side's 4-0 defeat by Barcelona in last weekend's Clasico.
But the position of the former Liverpool manager would have been placed under further scrutiny had Real failed to beat the smallest club in La Liga and lost more ground in the title race.
Seventh-placed Eibar had lost only twice in the league this season and held their own for long periods.
But despite fielding a makeshift defence missing the injured Sergio Ramos, Raphael Varane and Marcelo, Real's lead was rarely threatened once Bale broke the deadlock before the interval.
Ronaldo missed good chances either side of the break when he had just goalkeeper Asier Riesgo to beat.
But he ended his frustration from the spot eight minutes from time after Dani Garcia brought down substitute Vazquez, as Real secured the result Benitez badly needed.
Benitez said: "We knew they were playing well, that they are an intense and aggressive team. That's why the victory has more merit.
"We are in November. We have had injuries and the games are getting tougher. We have a great team and we are going to keep fighting until the end."
Valencia had defender Joao Cancelo and midfielder Javi Fuego sent off either side of half-time as they lost 1-0 to Seville .
Afterwards, Valencia coach Nuno Santo confirmed that he would be leaving his position.
Villarreal missed the chance to move into the top four as a 2-0 defeat at Getafe means they have won only one of their last seven league games.
Angel Lafita and Alvaro Vazquez scored the goals which lifted Getafe four points clear of the relegation places.
Striker Aritz Aduriz, 34, scored a hat-trick and took his total for the season to 20 goals as Atletico Bilbao won 3-0 at Rayo Vallecano .