The Argentine opened the scoring with a contentious penalty awarded for handball and then sealed victory for the visitors with a stooping header from a corner
The incredible Messi now has 43 goals in all competitions in another astonishing season after opening the scoring with a first-half penalty and heading home a second goal after the break in the Catalan giants' first trip to Estadio Municipal de Ipurua on Saturday.
Barca had the opportunity to increase their lead at the summit with Real Madrid not in action until they face struggling Levante on Sunday and, despite not being at their fluent best, did enough to pick up all three points thanks to the irrepressible Messi.
The leaders can now turn their attention to a key week in which they face Manchester City in the UEFA Champions League on Wednesday, before locking horns with second-placed Real in a top-of-the table El Clasico at Camp Nou next Sunday.
While Barca appear to have hit form at the right time, Eibar have now lost their last eight games and Gaizka Garitano's side look set for a battle to avoid relegation.
Barca star Neymar returned after serving a ban, but Barca full-backs Dani Alves and Jordi Alba were unavailable due to suspension as Luis Enrique rung the changes with City and Real no doubt in mind.
Ivan Rakitic was one recalled to the visitors' starting line-up, and the midfielder came close with a header in their first attack.
Eibar were clearly not overawed by the challenge of facing in-form Barca despite being on a dreadful run, and the Catalan giants found it difficult to break the home side down until they were awarded a penalty just after the half-hour mark.
Borja Ekiza was the guilty party as he handled Messi's strike and although Jaime went the right way, he was unable to keep out the resulting spot-kick from the Argentina captain.
Ekiza made a timely intervention to clear the danger after Messi raced into the penalty area and cut the ball back from the byline, and Luis Suarez slid in and fired a shot off target just before the break as Barca finished the first half strongly.
Neymar could have doubled Barca's lead seven minutes into the second period, but Jaime did well to come off his line to deny the Brazil forward after Messi had played him in with a lovely pass.
Barca did not have long to wait for a second goal, though, and yet again it was Messi on target as he met Rakitic's corner with a stooping header that bounced up off the slick turf and found the back of the net 10 minutes into the second half.
Xavi came on to replace Rakitic to make his 750th competitive appearance for Barca midway through the second half with the points seemingly secured.
Eibar showed plenty of fight but lacked the class to break down Barca - although Federico Piovaccari hit the bar in the 89th minute - and Luis Enrique can now turn his attention to two huge home matches against City and Real.