Levante marked its return to the Spanish league after a season away with a 1-0 win over Villarreal on Monday.
Jose Luis Morales converted an 88th-minute penalty kick at Ciutat de Valencia Stadium.
Morales himself earned the penalty kick after being fouled by defender Antonio Rukavina inside the area.
Levante played six straight seasons in the first division before being relegated last year.
Brazilian striker Charles gave Eibar the victory against former club Malaga with a 57th-minute header.
Charles played for Malaga the last two years before signing with the Basque Country club this season.
He put his hands together and raised his arms after scoring, apparently asking for forgiveness to the fans at Malaga's La Rosaleda Stadium.