With huge gaps in the stands suggesting the locals had already made up their minds after three straight defeats, Barca lacked their usual cutting edge and fell behind to Aritz Aduriz's 50th-minute strike, but turned it around with two goals in three minutes from Pedro and Lionel Messi with a quarter of an hour to go.
The result keeps Barca alive in the title race, but also answers some of the critics who were turning not only on Martino but also Cesc Fabregas and even Messi himself.
"The circumstances weren't in our favour but we came from behind and won," Martino said.
"In addition to our football, we relied on our courage to fight back."
Martino had returned to a more familiar shape with three in attack, with Alex Song preferred to Fabregas who came off the bench in the 70th minute, moments before Barca's double strike.
Messi had been quiet for most of the match, missing a couple of chances he would normally be expected to bury, but came up with the winning free-kick in the 75th minute.
"I'm very pleased for Messi because he defended himself the best way he knows how, on the pitch and not with words," Martino said.
The sight of Fabregas on the bench did little to quiet growing speculation about his future at Barca, and he heard boos when he was preparing to come on.
However, Martino stood up for the midfielder.
"I've no opinion of the whistles at Cesc," he said. "He has great character and always wants to play, always wants the ball and isn't afraid to make mistakes. He is brave."