The victory has also extended Barcelona's record-breaking unbeaten run to 36 matches in all competitions and moved the Catalan outfit 12 points clear of third-placed Real Madrid on the same number of matches.
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Barcelona were without Neymar through suspension, but Dani Alves and Jordi Alba both returned after missing Thursday's win over Rayo Vallecano, while Arda Turan started ahead of Andres Iniesta in the middle of the park.
Two minutes later, Suarez, whose movement was too sharp for Eibar's backline, might have made it 2-0 after being set away by Alba, but the striker missed the post, before Ivan Ramis headed over the crossbar down the other end.
David Junca was next to try his luck for the home side in the 21st minute, but the full-back's volley from close range was always moving wide of the post as Barcelona continued to dominate possession of the ball.
Barcelona should have had a second in the 31st minute when Messi scooped a pass into Munir, but the Spaniard attempted to cross towards Suarez and the ball drifted wide of the post.
The visitors' best spell of the first period came in the build-up to the break and Sergio Busquets just managed to turn a Sergi Enrich cross wide of the post, but Eibar were hit with a killer blow on the counter-attack when Messi drove into the box and found the bottom corner for 2-0 in the 42nd minute.
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It took until the 54th minute for Barcelona to carve out a chance in the second period, but a rare heavy touch from Messi prevented the Argentine from having a clear shot on goal after an excellent run and pass from Suarez.
Messi had another half-chance moments later, but could only poke wide of the post under pressure from Capa. In the 65th minute, Adrian Gonzalez tried his luck for Eibar, but his effort from distance was always high of the crossbar.
Barcelona had their third in the 75th minute, however, when Messi converted from the penalty spot after Ramis had been penalised for a handball inside the box.
It got worse for Eibar in the 84th minute when Suarez put the ball through the legs of Capa before finding the bottom corner to make it 36 games unbeaten for the Catalan giants.