Barca’s 11th straight win kept them eight points ahead of second-placed Atletico Madrid, who won 3-1 at troubled Valencia.
There was little chance of Barca dropping points in Eibar, after youngster Munir gave them the lead in the eighth minute following a clever combination down the right between Lionel Messi and Luis Suarez.
Munir, 20, was standing in for the suspended Neymar. The much-lauded “MSN” trio of Messi, Suarez and Neymar have now put away 100 goals this season in all competitions.
Eibar came close to an equaliser on three occasions in the first half, but against the run of play Messi made it 2-0 just before the interval with yet another trademark run and left-footed drive.
Messi scored what was his sixth goal in three games with a cool penalty in the 74th minute, after Eibar defender Ivan Ramis had handled a cross from the little Argentine.
Watch Messi’s goals below
Suarez completed the rout for Barca six minutes from time with a handsome solo goal.
Suarez, with 26 goals, is one behind Cristiano Ronaldo of Real Madrid in the Liga scorers’ chart.
It was Barca’s 11th straight league win and their first clean sheet since February 7 in La Liga, extending their record-breaking unbeaten run to 36 games.
After their win, Eibar coach Jose Mendilibar said his side had no hope of stopping Messi.
“When Messi is playing it’s impossible, he creates goals out of nothing,” he said.
“I wasn’t surprised by them, but there’s something about watching them up close. They never miscontrol a pass, in that sense they are superior to every other team.
“But what amazes me most is their defensive work. They can defend with six or seven players and leave three players up front.”