La Liga's reigning champions have now drawn two and won three of their opening five games.
The draw at Bilbao came after Barcelona beat Real Sociedad 4-2 last weekend in its first match since the club had to let Lionel Messi walk away to sign for Paris Saint-Germain
Atletico leads defending champion Real Madrid by two points with two matches remaining and will win the title if it beats Osasuna at home and Madrid fails to win at Athletic Bilbao.
Sevilla still holds a 17-point advantage over fifth-placed Real Sociedad and has secured a Champions League spot for next season.
Even though Messi avoided the burning question of his plans, his great game will raise hopes for Barcelona fans of the soccer great staying at Camp Nou.
The cup was won and lost in a whirlwind 12 minutes in Seville, which saw Barca score four times to clinch an emphatic 4-0 victory, with Messi at his devastating best.
Ernesto Valverde resigned from Athletic Bilbao on Tuesday with the hope of taking over at Barcelona next season.