"Chaco" Gimenez, one of the most respected players in the MX League, who has played in Mexico since 2004 and recently became a naturalised Mexican, laid on the opening goal for Joao Rojas with a trademark run and pull back after half an hour.
In a second-half downpour during Saturday's match at the Estadio Azul, Rafael Marquez Lugo equalised with a penalty before Ecuador forward Rojas and Jeronimo Amione scored two goals in the final 10 minutes to give Cruz Azul the win.
The 32-year-old Gimenez, who began his career at Boca Juniors, earned his national team call-up on Friday in what media regard as a key decision by the under-fire De la Torre to boost the creative department of his underperforming team.
De la Torre's job has been on the line due to mediocre results in the World Cup qualifiers, a poor Confederations Cup in Brazil in June and failure to retain the CONCACAF Gold Cup title in the United States last month.
Gimenez is expected to make his international debut in Wednesday's friendly against Ivory Coast in New York ahead of a World Cup qualifier at home to Honduras at the Azteca on September 6.
"I'm not Messi, I'm one more player and I'm going to try to help. My calling card is my commitment. I'm not a fireman, I'm a footballer and have to give of my best," he said in answer to suggestions that he would be Mexico's saviour.
Another Argentine-born player, 34-year-old UANL Tigres forward Damian Alvarez, was also picked, with a chance to win his second cap, as De la Torre goes for experience in his bid to put Mexico back on track.
Mexico are third in the final, six-nation CONCACAF group with eight points from a win and five draws, five points behind leaders United States and three short of Costa Rica. Honduras are fourth on seven points.
The top three teams go through to the 2014 finals in Brazil and the fourth-placed team will play off against Oceania winners New Zealand for another berth in the tournament.