Carlos Salcido crashed a long-range effort against the crossbar and Andres Guardado shot narrowly wide as Mexico found space in front of an Argentina backline that many believe to be a possible weak link in an otherwise gifted side.
Deportivo took control after the half-time break when Guardado put them ahead with a brilliant left-footed drive in the 55th minute and Diego Colotto wrapped up the points when he rifled in a low shot on the edge of the box after Tenerife again failed to clear a set-piece.