Barca coach Ernesto Valverde was without the injured Ousmane Dembele after the club's record signing was ruled out for up to four months with a torn hamstring and he opted to rest several regulars such as Luis Suarez and Ivan Rakitic, but that mattered little as Messi stepped up and produced an irresistible performance.
Barca were actually quite sluggish during the early exchanges, but they soon clicked into gear broke the deadlock, as Messi stylishly converted a penalty 20 minutes in to take his 2017 tally to 40 goals in as many games.
Paulinho, making his first LaLiga start, then answered his critics again just before the break, heading in Barcelona's second of the contest to add to his winning goal at Getafe on Saturday.
Denis Suarez got Barca's first at Getafe and he followed Paulinho's lead in scoring for the second successive game with a smart finish inside the near post early in the second half, just a few moments before Sergi Enrich pulled one back.
But Messi then stepped up, scoring twice in quick succession to blow Eibar away and complete his hat-trick - his second of the season after putting three past Espanyol.
The five-time Ballon d'Or winner was not done there as he added a sixth three minutes from the end to leave Eibar on the end of a truly emphatic hammering.
Barcelona came out to an expectant Camp Nou crowd donning shirts with "courage Ousmane" emblazoned across the front following Dembele's injury at Coliseum Alfonso Perez.
But the supporters were given cause for concern just three minutes in, when David Junca's curled pass picked out the run of Enrich in behind Gerard Pique, only for the striker to hit a tame effort at Marc-Andre ter Stegen when one-on-one.
Barca duly punished that miss, as Messi nonchalantly tucked away a spot kick after Alex Galvez clumsily sent the impressive Nelson Semedo tumbling.
Marko Dmitrovic denied Messi nine minutes before the break, palming a stinging 20-yard drive around the post.
But the goalkeeper was helpless from the resulting corner as Paulinho charged into the danger zone and met Denis Suarez's delivery with an unstoppable header.
Barca looked more impressive after the break and were fully deserving of their third goal.
Paulinho initially did well to release Messi, who dazzled the Eibar defence and got a shot away, with Dmitrovic parrying it straight to Denis Suarez to tuck away.
Enrich pulled one back with a clever cushioned finish from Junca's cross shortly after in the 57th minute, but all that seemed to do was jolt Barca into life again.
Messi took centre-stage, restoring Barca's three-goal cushion with a fine placed finish into the bottom-left corner from the edge of the box, following a delightful move which involved Sergio Busquets and Andres Iniesta.
And he then completed his hat-trick with 27 minutes to go, charging in from the right-hand side of the penalty area and prodding an effort beyond Dmitrovic.
Eibar nearly got a second when Ruben Pena hit the post late on, but Messi soon showed them how it should be done, as he met Aleix Vidal's cut-back and guided a finish into the far side of the net to wrap up a crushing win.
