Toni Kroos got Real off to an ideal start at the empty stadium based at their training ground by scoring in the fourth minute while captain Sergio Ramos struck on the half-hour mark before Marcelo netted in the 37th.
Real did ease off after the interval and Eibar forward Sergi Enrich struck the woodwork before Pedro Bigas pulled a goal back for the visiting side on the hour mark.
Real coach Zidane used all five of his substitutions as his players continued to tire.
The win kept Real on La Liga leaders Barcelona’s heels with 59 points after 28 games. They are two points behind Barca after the Catalans beat Real Mallorca 4-0 on Saturday.