The 2-0 victory kept Madrid in touch with Barcelona in La Liga — a week after a 4-0 humiliation against its fierce rival.
In the English Premier League, Chelsea and Arsenal were both held to draws.
Here is a look at Europe's major leagues on Sunday:
Benitez wasn't the only one to get a much-needed boost from the win against Eibar.
Bale also needed a good performance after three months without scoring a goal for Madrid. He ended his scoring drought by heading in Luka Modric's cross just before halftime, and Ronaldo brushed off two uncharacteristic misses by converting a late penalty, awarded when substitute Lucas Vazquez went down after slight contact with Dani Garcia.
Madrid remained in third place, six points behind leader Barcelona and two points behind Atletico Madrid.
While Benitez got some relief, Valencia manager Nuno Espirito Santo is set to step down after his team finished with nine-men in a 1-0 loss at Sevilla.
Espirito Santo said after the match that it "has been an honor" to coach Valencia and that he would meet with the club on Monday to finalize a decision that he said he had already discussed with owner Peter Lim. Valencia captain Dani Parejo later said on Canal Plus television that Espirito Santo told his players that he was "resigning."
Aritz Aduriz scored a hat trick to lead Athletic Bilbao to a 3-0 rout at Rayo Vallecano, and Getafe beat visitors Villarreal 2-0.
It's a sign of how dismal Chelsea's title defense has been that Jose Mourinho called a 0-0 draw at Tottenham the best performance of the season. A 1-1 draw for Arsenal at Norwich, though, left Arsene Wenger experiencing the same old frustrations.
Yet it is Arsenal sitting fourth in the Premier League — only two points behind leaders Manchester City and Leicester — and Chelsea is back in 14th place.
Arsenal's Alexis Sanchez, who later was forced off with a thigh injury, set up Mesut Ozil on the half-hour mark, only for Lewis Grabban to level before halftime. Defender Laurent Koscielny and Santi Cazorla were also hurt for Arsenal.
Liverpool moved within four points of Arsenal as Juergen Klopp earned his first league win at Anfield since replacing Brendan Rodgers as manager. James Milner's second-half penalty secured the 1-0 victory over Swansea following Neil Taylor's handball.
West Ham also drew 1-1 at West Bromwich Albion.
Juergen Kramny got off to a bad start as interim Stuttgart coach when Gonzalo Castro scored in the third minute and then set up Aubameyang in the 19th.
Aubameyang claimed his second of the match and 17th league goal of the season in injury time.
Dortmund stayed eight points behind leader Bayern Munich.
Third-place Wolfsburg could only manage a goalless draw at Augsburg.
Bayer Leverkusen also salvaged a 1-1 draw with Schalke after a late own goal by Sascha Riether.
Five days after a humiliating 6-1 rout by Barcelona in the Champions League, Roma's defensive deficiencies were highlighted again in an alarming 2-0 loss at home to Atalanta in Serie A.
Alejandro Gomez intercepted a poor pass from Roma defender Lucas Digne to score from outside the area before halftime. Then substitute fullback Maicon was sent off for tripping Gomez to set up a penalty for German Denis eight minutes from the end.
Roma remained fourth, wasting a chance to pull level with leader Inter Milan.
Four-time defending champion Juventus won 3-0 at Palermo for its fourth straight victory and moved into fifth.
Elsewhere, Empoli beat Lazio 1-0, Udinese won 3-2 at Chievo Verona, and Carpi came from behind for a 2-1 victory at 10-man Genoa. Hellas Verona remained winless after a 3-2 loss at Frosinone.
Defender Damien Da Silva scored twice as surprise package Caen climbed to second place in the French league with a 4-1 rout of Bordeaux.
Caen defender Syam Ben Youssef put the visitors ahead in the sixth minute. Da Silva then scored twice in the space of four minutes — 57th and 61st — before Andy Delort made it 4-0.
Another defender scored another brace as Monaco right-back Almamy Toure found the net twice in a 3-3 draw at Marseille.
Saint-Etienne defeated Guingamp 3-0 to move level on points with fourth-place Lyon.