The Argentina international opened the scoring for Barca from the penalty spot after Alejandro Galvez barreled over Nelson Semedo in the area and the referee pointed to the spot.
And Messi nearly doubled the lead minutes later, forcing Eibar goalkeeper Marko Dmitrovic into a diving save from his curling left-footed shot from the top of the box.
Paulinho then rose highest to reach a Denis Suarez corner kick and send a glancing header past Dmitrovic to put Barcelona up 2-0 before the break.
And Suarez added to Barca’s lead soon after the break, slotting home from close range after Dmitrovic had saved a Messi shot coming on the counter-attack.
Eibar clawed one back a few minutes later against the run of play, Sergi Enrich doing well to poke home a pinpoint cross from David Junca to make it 3-1.
But just like that, Messi restored the three-goal lead, beating three men at the top of the penalty area and calmly despatching a left-footed strike into the back of the Eibar net.
The rout was well and truly on for Barca by now and Messi completed his hat trick just past the hour mark, chipping the ball past Dmitrovic with the outside of his foot as two Eibar defender dragged him down.
And Messi would add his fourth — for the sixth time in his career — as full-time approached, deftly redirecting a Aleix Vidal pass into the back of the net to cap his third multi-goal game for Barca in just five tries this season.
Barcelona will now ready for a Saturday trip to Girona in their next match.
Simone Zaza scored a hat trick inside nine minutes as Valencia routed Malaga 5-0.
The Italy international, who experienced an ill-fated loan spell with West Ham last year, struck three times between the 54th and 63rd minutes after Santi Mina had opened the scoring for Valencia, with substitute Rodrigo adding a fifth late on.
Los Che maintained their unbeaten record, though this was their first win in four games, against a Malaga side who have opened their league campaign with five defeats from five.
Zaza had already had one goal disallowed for offside when Mina headed home the 17th-minute opener and it remained 1-0 until the break.
Zaza’s rapid hat trick then took the game beyond Malaga and he was taken off for Rodrigo, who rounded it off with a fifth after a cheeky back-heeled pass from Goncalo Guedes to set him up.
Information from Press Association Sport was used in this report.