Eibar went into the game needing a win to move back into the European places and continue the most unlikely of dreams, whilst Barca were looking to re-establish their lead at the top of La Liga following two straight draws.
Despite Barca going full strength it was the hosts who got off to the better start, with Cote heading over inside a minute.
Jordi Alba saw an effort well blocked away by a visiting defender after Luis Suarez had rounded Marko Dmitrovic before the hosts continued their early pressure.
Kike Garcia saw a low effort from a narrow angle well saved by Marc-Andre Ter Stegen before Ivan Ramis could only direct a header straight at the German.
- Against the run of play -
With 16 minutes of the game gone, Barca took the lead against the run of play.
Lionel Messi was allowed to turn on halfway and he sent Suarez scampering away with a fine pass, with the Uruguayan keeping his cool to round Dmitrovic and roll the ball into the empty net.
Despite the setback, Eibar continued in the same vein and almost found an immediate response as Fabian Orellana thumped a curling effort against the crossbar from 25 yards.
As the first half wore on Joan Jordan wasted a good shooting chance by dragging an effort well wide of the near post under little pressure.
Despite Eibar’s dominance it was Barca who came closest as the half drew to a close, Brazilian midfielder Paulinho only managing to head straight at Dimitrovic in the home goal after meeting Alba’s cross, before Messi rattled the post after being fed by Suarez.
Nevertheless, the two sides went into the break level and there continued to be little between them in the second half.
The second period continued in the same vein, with Eibar enjoying the better of things and Barca threatening on the counter.
Suarez blazed well over the bar after being fed by Messi, before Takeshi Inui curled wide of the far post after meeting a cutback from the left.
- Turning point -
Eibar’s hopes of getting something out of the game were all but ended after 66 minutes though after a moment of madness from Fabian Orellana. The Chilean, who had only been booked eight minutes earlier, threw the ball away after seeing a team-mate booked and was promptly issued with a second yellow card and given his marching orders.
Gaps started to appear in the home defence at the game went on, though Dmitrovic was there to plug the leaks. Messi looked certain to score after being put in by substitute Philippe Coutinho, but Dmitrovic made a fine save to deny the Argentine's attempted chip, before making another stop to deny Aleix Vidal just minutes later.
With just two minutes to go Barca made the game safe. Vidal cushioned a pass from Coutinho into the path of Messi and whilst Dmitrovic denied him once again, the loose ball fell to Alba to slot home at the near post.
The win sees Barca equal the clubs longest ever La Liga unbeaten run, hwilst they also move 10 points clear of Atletico Madrid in second, albeit having played a game more, as they now move on to the game against Chelsea in midweek. Eibar certainly deserved more form the game but were left empty handed and remain in 7th.