Valverde's team have now equalled a club record by going 31 La Liga games unbeaten and enjoy a 10-point lead at the summit, at least until Atletico Madrid host Athletic Bilbao on Sunday afternoon (Monday morning AEDT).
Luckily for Barca fans - and football lovers in general - Lionel Messi and Luis Suarez are sure-fire choices and are rarely dropped, even when a crucial fixture like Tuesday's game against Chelsea awaits.
The Chilean was, though, sent off on 66 minutes for punching the ball away, before Mendilibar, taking charge of his 100th LaLiga game with Eibar, was dismissed for protesting to the fourth official and Jordi Alba added Barcelona's late second.
Paulinho almost made it 2-0 nine minutes before the break after he was picked out by Jordi Alba with a cross but his header could not find the target from inside the box.
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The Catalan giants remain unbeaten this season and still maintain a healthy seven point lead at the top of table. Valverde's team showed again their fighting spirit and ability to grind out results, and it sets them up nicely for their trip to Chelsea in the UEFA Champions League on Tuesday.
An exquisite through-ball from Lionel Messi gave Suarez the chance to round Marko Dmitrovic and tuck the ball over the line for goal number 17 of the La Liga campaign.
The loss was only the second for Eibar in its last 13 matches.
Chelsea thumped Hull City by a margin of four goals despite missing many big names.
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Indeed, Torino have only one Derby della Mole win since 1995 and while the home crowd always relish this occasion, their team hasn't looked like one capable of troubling Juve.
"Against opposition like them there's no formula to it, the key is for us to just be ourselves, be assured and not have any doubts about what we have to go out there and do".
It is a remarkable turnaround from their dismal form at the start of the season when they lost seven of their first 11 games, although coach Jose Luis Mendilibar said his side had barely altered their style, which is based on pressing high, no-nonsense defending and frequent crosses into the opposing box. "We know it will be hard and that we have to play smart for 180 minutes". Orellana compounded that mistake when he batted a ball into the air with play stopped and the referee waiting for Eibar to return the ball to Barcelona to take a free kick.
Earlier, Sevilla warmed up for their Champions League clash with Manchester United by winning 2-1 at Las Palmas, aided by a controversial late offside call.
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Barcelona will have their minds set on their upcoming tie against English champions Chelsea. Draws with Espanyol and Getafe came after being pushed to the limit by Alavés the week before.