After Malaga had fought back from a goal down to take a 2-1 lead at the Anoeta, Carlos Vela struck in the 89th minute and Diego Ifran netted the winner two minutes later to lift Sociedad, coached by Frenchman Phillipe Montanier, to 13th.
Qatar-owned Malaga, one of Europe's biggest spenders in the close season transfer market, are fifth with 23 points, three behind Levante who were thrashed 5-0 at champions Barcelona on Saturday.
"It hurts to lose a game in the final three minutes," Malaga coach Manuel Pellegrini told a news conference.
"We had controlled this match," the Chilean, Jose Mourinho's predecessor at Real Madrid, added.
"It's not up to me," Mel told a news conference when asked about his future.
"If they want me to carry on I'll carry on," he added. "If not I have a very clear conscience."
