Barca twice came from behind to salvage the point on Tuesday night. They had won five straight in La Liga after opening with a draw at Getafe and also won their Champions League debut against Royal Antwerp last week.
The result left the Catalan club in danger of relinquishing top spot when the remaining midweek games are played. They lead Girona by one point and Real Madrid by two, with Girona visiting Villarreal on Wednesday and Madrid hosting promoted Las Palmas.
"We conceded two goals after defensive mistakes and we can't allow that to happen," Barcelona coach Xavi said.
"It's a shame, we lost two points because of these mistakes."
Mallorca, who squandered a few good chances on counterattacks, has just one win so far and are 15th with six points and were coming off a 5-3 loss at Girona.
"It was a fair result, we are satisfied," Mallorca's Mexican coach Javier Aguirre said.
"A victory would have been too much for us today."
The hosts opened the scoring through Vedat Muriqi in the eighth minute before Raphinha equalised in the 41st. Abdon Prats put Mallorca ahead again just before halftime and Fermin Lopez sealed the draw in the 75th with what was his first league goal for the Catalan club.
Barcelona had a penalty kick awarded in the 66th minute, but the decision was reversed after video review.
Elsewhere, Sevilla scored twice in the first 10 minutes and went on to rout Almeria 5-1 for their second league win of the season.
Youssef En-Nesyri netted in the seventh minute and Dodi Lukebakio in the eighth, then Suso added another in the 38th before Erik Lamela and Kike Salas closed the scoring in the second half.
It was the fifth loss for Almeria, who remain bottom and the only team yet to win a match.
Almeria next host Granada, while Sevilla visit Barcelona.
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