 Athletic Club Bilbao's players |
A Gerard Pique own-goal looked to have condemned Barca to a first defeat this season in the 80th minute before the World Player of the Year netted his 14th goal of the campaign at the death.
Barca keeper Victor Valdes was beaten for the first time in 10 matches when Ander Herrera fired Bilbao in front in the 20th minute, but Cesc Fabregas headed the visitors level just four minutes later.
The European and Spanish champions remained second on 25 points, three behind Real Madrid, who crushed Osasuna 7-1 earlier in the day with a hat-trick from Cristiano Ronaldo.
The world's most expensive player paraded the Golden Boot before kickoff for the 40 league goals he scored last season, and he helped his bid to win it again with another sparkling performance at the Bernabeu.
Argentina winger Angel Di Maria set up the first three goals for Ronaldo, Pepe and Gonzalo Higuain before being carried off with a torn thigh muscle at the start of the second half.
Ronaldo notched his second goal from the penalty spot in the 54th when Osasuna had defender Eneko Satrustegui sent off, and he completed his fourth league treble this season in the 57th, taking his La Liga tally to 13.
Substitute Karim Benzema wrapped up the scoring with two more goals.
Injury-hit Osasuna, thrashed 8-0 away to Barcelona in September, had drawn level at 1-1 in the 31st minute when Ibrahima took advantage of a quickly-taken free kick to beat Iker Casillas.
Valencia are third with 24 points after winning the city derby 2-0 at Levante on Saturday, pushing the season's surprise early pace-setters down to fourth with 23 points.