The Ivory Coast international, signed from Barcelona in the summer, looked impressive throughout as City dominated the first half.
The Blues led at half-time thanks to a Emmanuel Adebayor penalty (36) after Adam Johnson was felled.
But City, who made six changes at the interval, were pegged back by the Mexican side two minutes into the second half through Enrique Esqueda. The game went to penalties and City won 4-1 with Shay Given saving twice.
In addition to Yaya Toure, City boss Roberto Mancini gave first outings of the summer to England World Cup players Shaun Wright-Phillips and Gareth Barry.
Both sides came close to adding to their tallies with Daniel Montenegro's drive from 25-yards skidding against Joe Hart's post in the first period while City thought they had won it in the 88th minute when Adebayor hit the underside of the bar with a volley.