The Argentine's opener came from the penalty spot in the first period and he headed in a second after 55 minutes.
The result has moved Barca four points clear at the top of the table, while Eibar remain 14th following their eighth straight league defeat.
Here, Sports Mole dissects the 90 minutes of action between the two Spanish rivals.
On target: 2
On target: 4
Was the result fair?
It was an extremely straightforward 90 minutes for Barcelona. Statistics in football rarely paint a false picture and the fact that Eibar had more shots than the visitors might raise a few eyebrows, but there was not really a point in the match when Barcelona were not in control. The first goal was always going to be vital and when it came for the league leaders, Eibar were already playing catch-up as they stared an eighth successive league defeat in the face. It was a fairly unfortunate penalty to concede, but replays demonstrated that Borja Ekiza had handled an effort from Messi. Despite the goal on 31 minutes, Eibar still enjoyed some bright moments, but struggled in terms of clear opportunities.
If the first goal was important, then the second was crucial. It did not take long for Barca to register in the second period, with Messi heading an Ivan Rakitic corner into the back of the net. From that moment, it was game over. Eibar had their moments in the final third and rattled the crossbar through Federico Piovaccari late on, but Barcelona always offered the impression that they could raise their performance if needed. They have won by more comprehensive scorelines this season, but this was still one of their most comfortable victories. It was the perfect match ahead of a massive couple of fixtures.
Eibar would have been forgiven for sitting back in the early moments due to their horror run of form, but, in fairness to the hosts, they took the game to Barcelona in the opening 20 minutes. Manu del Moral did a good job of running the lines, while Saul Berjon showed flashes of ability in the final third. They were also nice and tight in defensive areas, but that came crashing down in the 31st minute when Messi converted from the penalty spot. It would have been easy for Gaizka Garitano's side to collapse in the latter stages of the first period, but they managed to stem the flow of pressure as the interval approached.
At 1-0 behind, they needed to score the next goal, but their challenge ended just 10 minutes into the second period. The fact that Barcelona's goals came from the penalty spot and a header from one of the smallest players on the pitch will be disappointing, but the visitors had more opportunities to put the game to bed. The home supporters stayed with their team, however, and were rewarded with a late rally. Eibar did not really do too much wrong in terms of individual errors or bad performances, they just came up against a side - and a player - that simply had far too much quality.
Ahead of their key Champions League clash with Manchester City next week, head coach Luis Enrique shuffled his pack, with Dani Alves, Javier Mascherano, Jeremy Mathieu, Jordi Alba and Andres Iniesta among those that did not start. Such is Barca's strength in depth, however, that they still boasted an XI that ultimately claimed the points in comfortable fashion. It was not the best of first-half performances, with Messi converting what was their only attempt on target, but there was not really a period of the match when they did not seem comfortable and in charge. When Messi scored his second, many felt that Barca would go on to win by four or five, but it did not come as much of a surprise when they dropped their level. The points were secure and they have more pressing matters over the next eight days.
The victory moved them four points clear of Real Madrid ahead of next weekend's El Clasico at the Camp Nou, but that is expected to be one point before the two teams take to the field, with Real hosting Levante on Sunday evening. Messi's two goals moved him ahead of a certain Cristiano Ronaldo in the La Liga scoring charts in what was another impressive performance. Luis Suarez and Neymar were both fairly quiet, but Messi had already done the damage. Overall, it was a night of positives for Enrique, but there were a couple of sloppy defensive moments that the Spaniard will be keen to address.
Sports Mole's man of the match
Lionel Messi: Not exactly the hardest decision to make. Messi is in stunning form at the moment and continued in a similar vein against Eibar with another two goals. The Argentine showed excellent composure to finish from the penalty spot before heading in a second after 55 minutes. The forward also produced a couple of outstanding dribbles, with the home side almost mesmerised by a player that has returned to his best form in 2015. Could he lead Barca to a treble this season?
It is perhaps a little harsh to be critical of Piovaccari, who was a real threat for Eibar upon entering the field, but the Italian really should have scored in second-half stoppage time. Barca's defence were caught out by a long ball and allowed Piovaccari time and space inside the box, but his effort smashed against the crossbar. It probably would have come too late to impact the outcome of the match, but it would have given the home supporters something to cheer.
Referee Carlos del Cerro will not have many more evenings as straightforward as this. The Spaniard issued just the one booking, which came for Ekiza when he handled inside the penalty box. The actual penalty incident was perhaps a shade harsh, but Del Cerro was in a good position and made a quick and decisive call. Aside from that, the official was hardly seen as he allowed play to flow in all areas of the field.
Eibar: Eibar's battle to overcome their horror run of form will continue with a trip to fellow strugglers Granada next Saturday.
Barcelona: Barca will attempt to book their spot in the quarter-finals of the Champions League when they welcome Manchester City for the second leg of their last-16 clash on Wednesday. Next Sunday, they welcome Real Madrid in the league.