Alexander Farnerud scored the only goal as Sweden pounced on a mistake by the Mexican defence in the 57th minute to leave Eriksson's side with only one win in their last six outings.
Juan Carlos Valenzuela gave the ball away as Mexico tried to play out of defence, Rasmus Elm accepted the gift and found Farnerud who scored with a left-foot shot.
Mexico were close to opening the scoring when Matias Vuoso hit the post in the 17th minute while goalkeeper Oswaldo Sanchez prevented Sweden taking a halftime lead when he turned away Daniel Nannskog's effort.
Carlos Ochoa had a header cleared off the line as Mexico pressed for an equaliser in the second half.
Mexico are away to the United States on February 11 in their first match of the final stage of the CONCACAF region's World Cup qualifiers.
Eriksson's side were nearly eliminated in the previous stage, sneaking through on goal difference from Jamaica and finishing behind Honduras in their group after losing to both teams. They were also held to a draw by Canada.
Eriksson has also been heavily criticised for fielding too many foreign-born players, although the coach says he is only following the rules and does not understand what the fuss is about.
Mexico started with three naturalised players on Wednesday - Argentine-born Lucas Ayala and Matias Vuoso and Brazilian-born Leandro Augusto.
Ayala was replaced in the second half by Antonio Naelson, another player born in Brazil.
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