Nicolas Otamendi headed the hosts in front on 25 minutes and Dani Parejo and Paco Alcacer extended their advantage with goals in the second half, with Mikel Arruabarrena getting a late consolation for Eibar.
The result sees Nuno’s side go three points clear of Sevilla and they are two wins away from Champions League football.
Eibar, meanwhile, remain in deep trouble on 31 points and hovering above the relegation zone.
Malaga’s poor run of form continued as they slumped to a 2-1 defeat at home to Elche in Sunday’s late kick-off.
Jonathas put the visitors in front in the first half, before they were reduced to 10 men inside the final 20 minutes as goalkeeper??Przemyslaw Tyton was dismissed for a foul on Javi Guerra, but Duda missed the chance to level things from the spot, firing his penalty against the post.
Jonathas then set up Mario Pasalic to make it 2-0 in the dying moments of normal time, before Guerra pulled one back in stoppage time after Nordin Amrabat’s spectacular effort hit the crossbar, but the visitors held on for the victory.
Espanyol and Rayo Vallecano’s hopes of qualifying for the Europa League were dented as they shared the spoils in a 1-1 draw at the Power8 stadium.
Emiliano Insua put the visitors ahead just before the half-hour mark but Hector Moreno grabbed a deserved equaliser with 10 minutes remaining, before Jose Canas was sent off in stoppage time for dissent.
Espanyol moved on to 46 points but missed the opportunity to go level with Athletic Bilbao in seventh spot, while Rayo earned a second consecutive draw and drop down to 12th.
Youssef El Arabi scored twice as Granada won 2-1 at Getafe to boost their chances of beating the drop and give Jose Ramon Sandoval a winning start as boss.
Granada responded to Thursday’s home defeat to Espanyol by replacing manager Abel Resino with Sandoval and the former Rayo Vallecano coach could not have asked for a better start.
El Arabi opened the scoring from the penalty spot after a quarter of an hour and headed home on the hour mark to earn Granada victory after Pedro Leon had equalised on the stroke of half-time.