Villarreal, meanwhile, followed up their impressive 1-0 win at Atletico with a comfy 3-1 home win over Gijon that means they stay in 5th, five points behind Sevilla who now occupy the final Champions League spot.
Villarreal is five points behind fourth-place Sevilla, the last team now securing a Champions League spot.
With 20 minutes left the game was still scoreless and Eibar were holding up well defensively.
Cedric Bakambu fired Villarreal level in the 32nd after beating the offside trap to latch on to a clever through ball from Roberto Soldado.
Neymar, who excelled in his incursions from the left flank throughout, opened the scoring when he poked in a shot by Messi that hit a defender and fell to him in front of goalkeeper Andres Fernandez.
However, it mattered little as Real maintained their ideal La Liga record in nine games without Ronaldo this season.
He said: "We have already chosen his replacement but we won't communicate our decision right now out of respect for Luis Enrique".
"We have to go out hard and try to win the second leg as well".
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The goals Messi scored in the match were his 50th and 51st whilst Barcelona's total in La Liga is now an impressive 108.
The Yellow Submarine have won five of their last six, including an away victory over Atletico Madrid, as they make a late bid for the fourth and final Champions League berth with Sevilla stumbling.
"Neymar is a player with exceptional characteristics", Pique told BeIn after the game.
Lionel Messi also scored twice against Villarreal and Luis Suarez was always on target as Barca's attacking trio took their combined total for the season past 100 for a third consecutive campaign.
"It's incredible, our fans are with us until the end", goalscorer Saul Niguez said.
Carlos Carmona got the only goal midway through the second half to move Sporting to within three points of Leganes with two games remaining. "They have the best players in the world and are fighting for the championship", said Argentine defender Mateo Musacchio, one of the main players in Villarreal's well-organized team. It's attractive, it's effective and it's spectacular.
The win came on the back of Atletico's midweek defeat to Real Madrid in the Champions League and following Sevilla's 1-1 draw at home to Real Sociedad on Friday.
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