The result sees Xavi’s side stay eighth in the table, 15 points behind leaders Real Madrid, who play later on Sunday.
Teenagers Nicolas Gonzalez and Abdessamad Ezzalzouli, both 19, scored for the visitors.
But the hosts twice fought back, with David Garcia and Ezequiel Avila ensuring they claimed a deserved point from the contest.
Barcelona had come into the fixture looking to make amends for consecutive defeats by Real Betis and Bayern Munich.
Midfielder Gonzalez, gave them a perfect start, racing on to Gavi’s superb pass and prodding past home goalkeeper Sergio Herrera to register his first goal for the club.
However, Garcia headed in an equaliser two minutes later after some non-existent marking from a set-piece and Barca, who are still suffering from a lengthy injury list, struggled to provide forward support to the isolated Luuk de Jong for most of the first period.
They did improve after the break and Ousmane Dembele’s driving run was rewarded as Ezzalzouli converted his cross from close range.
With the clock ticking down it appeared to have put them on course for a much-needed victory until Avila drove in from the edge of the penalty area