But two goals mid way through the second half from Luis Suarez and Ousmane Dembele secured the points for the Catalans who sit top of the table to points ahead of Real Madrid who drew 1-1 at Athletic Bilbao.
"The league is defined by these kind of games," Suarez said afterwards. "Last year we also came back from 2-0 after many years without winning here. The reaction says a lot about this team."
Valverde had made the surprise decision to omit Sergio Busquets from his starting line-up. But he was introduced in the second period along with Philippe Coutinho.
"In the first half they closed us down well but Philippe coming on in the second half helped changed the dynamics," Suarez said.