Lapuente, who led Mexico to the second round at the 1998 World Cup, had been in charge of the Monterrey-based club for just under a year and became the third coach to lose his job in seven rounds of matches.
Tigres have taken six points from seven games and are fifth in Group Three.
America's win was their first in three games under new coach Jesus Ramirez, who replaced Argentine Ramon Diaz after four matches of the championship.
Titleholders Toluca remained unbeaten as they drew 1-1 at home to Tecos UAG.
Chile striker Hector Mancilla, the championship's leading scorer with six goals, missed a penalty for Toluca with 10 minutes left.
Edgar Duenos headed in Antonio Naelson's cross to give Toluca a sixth-minute lead and Claudio Graf equalised for the Owls five minutes later after a one-two with Rodrigo Ruiz.
Toluca lead Group Three with 15 points and Tecos top Group Two with 10.
Pachuca, the only other unbeaten team in the competition, stayed top of Group One with 17 points after beating Ciudad Juarez 3-0.
The 18 teams play each other once in the qualifying stage but are divided into three groups.
