Real Madrid won the match 2-1.
The victory moves Real four points within second-placed Atletico Madrid.
Heading closer towards the business end of the season and with Madrid qualifying for the quarter finals of the Champions League, Zidane and the Madrid fans will be hoping to have Varane back sooner rather than later for what could be Real's only chance at silverware this season.
But Ronaldo proved the difference again, the 33-year-old taking his tally for the season to 35 goals in 37 appearances.
"You've got to recognise the performance from Eibar, who put in a great display", Zidane added.
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Isco saw a 23rd minute shot blocked inside the Eibar box, but after Joan Jordan saw his header from a Pedro Leon free-kick fly just wide of the target, Real found themselves in the lead, very much against the run of play.
Ronaldo put the European champions ahead in the 34th minute following a lovely pass from Luka Modric.
From the resulting corner, Bale got above the Eibar defence, only to divert his glancing header wide of the post, but the opportunity suggested that the visitors were starting to up the tempo.
Lucas Vazquez and Karim Benzema replaced Isco and Toni Kroos as Zidane looked to raise the tempo and find a second goal.
Raphael Varane is now under observation by Real Madrid's medical staff after being forced off with a head injury in Saturday's LaLiga win at Eibar.
First, the unmarked Inui headed over from seven yards out and then Kike hit the side-netting with only Keylor Navas to beat.
Eibar conceded possession in manner like they did in the build-up to Real's first goal and the Portuguese nodded home the crucial goal off a Dani Carvajal cross.