The Spaniard had been at fault for Eibar´s equaliser earlier in the second half, allowing Ivan Ramis to head in an equaliser from a corner.
Victory means Zinedine Zidane's side have won eight of their last nine matches in all competitions, but still trail La Liga leaders Barcelona, who have a game in hand, by 12 points.
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.
They were below their best and rode their luck late on when Eibar should have converted a pair of excellent chances, before Ronaldo made them pay.
But Ronaldo proved the difference again, the 33-year-old taking his tally for the season to 35 goals in 37 appearances.
Valencia tightened their grip on fourth place in the standings and took a giant leap towards returning to the Champions League by winning 2-0 at Sevilla, opening up an 11-point gap with the Andalusians in fifth place.
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Ramos nodded the ball into the bottom corner after meeting Pedro Leon's corner.
Ramos went off on minute 73 before Ronaldo had scored his second goal to give Real Madrid all three points in a 2-1 win.
Madrid coach Zinedine Zidane sent on Karim Benzema and Lucas Vazquez to look for the victor. His whipped cross found the leaping Ronaldo and the Portugese made no mistake.
Real Madrid's form prior to the last 16 clash against the French giants raised many questions as to whether they could withstand the attacking strength of Unai Emery's side.